Safe and energy efficient
predictive cruise control
behind a slow-moving vehicle
Model predictive control for energy optimization

Master’s thesis in Systems, Control and Mechatronics

Johnny Truong
Venkatraman Nagaraj



Department of Electrical Engineering
CHALMERS UNIVERSITY OF TECHNOLOGY
Gothenburg, Sweden 2019

ii





Master’s thesis 2019

Safe and energy efficient predictive cruise control
behind a slow-moving vehicle

Model predictive control for energy optimization

Johnny Truong
Venkatraman Nagaraj

Department of Electrical Engineering
Chalmers University of Technology

Gothenburg, Sweden 2019



Safe and energy efficient predictive cruise control behind a slow-moving vehicle
Model predictive control for energy optimization
Johnny Truong
Venkatraman Nagaraj

© Johnny Truong, Venkatraman Nagaraj, 2019.

Supervisor: Esteban Gelso, Volvo Group Trucks Technology
Examiner: Nikolce Murgovski, Department of Electrical Engineering

Master’s Thesis 2019
Department of Electrical Engineering
Chalmers University of Technology
SE-412 96 Gothenburg
Telephone +46 31 772 1000

Cover: The Volvo Concept Truck [1]

Typeset in LATEX
Gothenburg, Sweden 2019

v



Safe and energy efficient predictive cruise control behind a slow-moving vehicle
Model predictive control for energy optimization
Johnny Truong
Venkatraman Nagaraj
Department of Signal and Systems
Chalmers University of Technology

Abstract
The goal of this project is to develop an MPC (Model Predictive Control) algorithm
which minimizes energy consumption for a controlled hybrid electrical vehicle while
keeping a safe distance to a leading vehicle.
The algorithm consists of two main parts: speed prediction and optimization. An
observer is first developed to estimate the power capability of the leading vehicle
which is used to predict its driving behaviour. With the information of leading
vehicle’s driving, a reference speed trajectory can then be obtained for the controlled
vehicle. The controller then minimizes the fuel consumption by finding the optimal
control and state trajectories based on the reference speed and the road topography.
The control signals include engine power, mechanical braking and power from electric
machine. The states include traveling time, speed and battery energy.
The work was conducted in Matlab where the control-algorithm was tested in simu-
lated driving scenario with measurement data of a heavy-duty leading vehicle driving
on a known topography. The obtained results showed decreased fuel consumption
with the hybrid electric vehicle compared to the conventional vehicle and manages
to keep safe distance from another vehicle in front. However, the significant fuel
reduction also exceeds results from previous works related to energy optimization of
hybrid electrical vehicle. More measurement data is needed to further validate the
performance of the control algorithm.

Keywords: Model Predictive Control, energy optimization, hybrid electrical vehi-
cle

vi





Acknowledgements
We would like to thank both our examiner, Nikolce Murgovski, and our supervisor,
Esteban Gelso, for giving us the opportunity to work on this thesis. We would also
like to thank the previous master thesis worker Mattias Hovgard who answered our
questions and problems during our work.

Johnny Truong, Venkatraman Nagararaj,Gothenburg, June 2019

viii





x



Contents

List of Figures xiii

List of Tables xvii

1 Introduction 1
1.1 Background . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2
1.2 Purpose . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
1.3 Objective . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
1.4 Delimitations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
1.5 Report outline . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3

2 Theory 5
2.1 Concept of MPC . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
2.2 Convex optimization problem . . . . . . . . . . . . . . . . . . . . . . 6
2.3 Vehicle model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6

2.3.1 ICE model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
2.3.2 EM model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11
2.3.3 Battery model . . . . . . . . . . . . . . . . . . . . . . . . . . . 13
2.3.4 Safety constraint . . . . . . . . . . . . . . . . . . . . . . . . . 14
2.3.5 Aerodynamic drag model . . . . . . . . . . . . . . . . . . . . . 15

3 Methods 17
3.1 Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17
3.2 Formulation of optimization problem . . . . . . . . . . . . . . . . . . 18
3.3 Control scheme . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19
3.4 Variable change . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20
3.5 Linearization and approximations . . . . . . . . . . . . . . . . . . . . 21

3.5.1 ICE model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21
3.5.2 EM model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22
3.5.3 Battery model . . . . . . . . . . . . . . . . . . . . . . . . . . . 23
3.5.4 Aerodynamic drag model . . . . . . . . . . . . . . . . . . . . . 23

3.6 Reference speed of host vehicle . . . . . . . . . . . . . . . . . . . . . 24
3.6.1 Leading vehicle observer . . . . . . . . . . . . . . . . . . . . . 24
3.6.2 Noise disturbance . . . . . . . . . . . . . . . . . . . . . . . . . 26
3.6.3 Leading vehicle reference speed predictor . . . . . . . . . . . . 28
3.6.4 Host vehicle reference speed predictor . . . . . . . . . . . . . . 28

3.7 Energy management . . . . . . . . . . . . . . . . . . . . . . . . . . . 29

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Contents

3.8 Power management . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30
3.8.1 Power split . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31
3.8.2 Dynamic Programming . . . . . . . . . . . . . . . . . . . . . . 33
3.8.3 Battery costate optimization . . . . . . . . . . . . . . . . . . . 33

3.9 Summary of MPC-algorithm . . . . . . . . . . . . . . . . . . . . . . . 35

4 Results 37
4.1 Validation of control algorithm without LV . . . . . . . . . . . . . . . 38

4.1.1 CV without LV ahead . . . . . . . . . . . . . . . . . . . . . . 38
4.1.2 HEV without LV ahead . . . . . . . . . . . . . . . . . . . . . 40

4.2 Validation of control algorithm with LV . . . . . . . . . . . . . . . . . 41
4.2.1 LV observer . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41
4.2.2 CV with LV ahead . . . . . . . . . . . . . . . . . . . . . . . . 42
4.2.3 HEV with LV ahead . . . . . . . . . . . . . . . . . . . . . . . 44

4.3 Length of prediction horizon . . . . . . . . . . . . . . . . . . . . . . . 46
4.4 No observer available . . . . . . . . . . . . . . . . . . . . . . . . . . . 49
4.5 Benefit of HEV . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53
4.6 Benefit of having prediction horizon . . . . . . . . . . . . . . . . . . . 53

5 Discussion 55
5.1 Leading vehicle observer and speed prediction . . . . . . . . . . . . . 55
5.2 Measurement data and road topography . . . . . . . . . . . . . . . . 56
5.3 Choice of prediction horizon . . . . . . . . . . . . . . . . . . . . . . . 56
5.4 Ethic and sustainability . . . . . . . . . . . . . . . . . . . . . . . . . 56
5.5 Future work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57

5.5.1 Measurement data . . . . . . . . . . . . . . . . . . . . . . . . 57
5.5.2 Computation time . . . . . . . . . . . . . . . . . . . . . . . . 57
5.5.3 Model and optimization controller . . . . . . . . . . . . . . . . 57
5.5.4 Road traffic and environment . . . . . . . . . . . . . . . . . . 57

6 Conclusion 59

Bibliography 61

xii



List of Figures

2.1 Simple block diagram of MPC. . . . . . . . . . . . . . . . . . . . . . . 5
2.2 The powertrain configuration of host vehicle which shows gear box, fi-

nal drive, ICE (Internal Combustion Engine), EM (Electric Machine)
and their power sources. ICE and EM are connected to same gears. . 6

2.3 Fuel consumption is shown as the function of torque for various engine
speeds. The measurements are shown in black and the fitted model
is shown as contour. The numbers on the graphs represent the engine
speed. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8

2.4 Torque limits and efficiency contour of ICE are shown as the function
of engine speed. The original torque limits are in black and fitted
torque limits are in red. The green line represents the maximum
power delivered by ICE. . . . . . . . . . . . . . . . . . . . . . . . . . 9

2.5 Longitudinal force that engine can deliver as function of vehicle speed
for different gears. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10

2.6 Torque limits as function of EM speed. The efficiency percentage is
shown as contour, original torque limits are in black and fitted torque
limits are in red. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12

2.7 Electrical power consumed by EM is shown as the function of torque
for various EM speeds. The original model is shown in black and the
fitted model is shown as contour. . . . . . . . . . . . . . . . . . . . . 13

2.8 The leading vehicle and host vehicle driving on road with hills which
is 7km long. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14

2.9 Comparison between measurement data and fitted model of aerody-
namic drag reduction fd(dLH). . . . . . . . . . . . . . . . . . . . . . . 15

3.1 The control scheme divided into two layers, energy and power man-
agement. Energy management estimates the optimal trajectories for
v and λB, which are then sent to the power management. The power
management in turn estimates the optimal trajectories for γ and χ,
which are then sent to energy management to estimate its optimal
state and control trajectories again. . . . . . . . . . . . . . . . . . . . 19

3.2 Acceleration as function of vehicle speed. The blue star points repre-
sent ameas and the black lines represent the speed-clusters. . . . . . . 25

3.3 Acceleration as function of vehicle speed. The blue star points repre-
sent ameas. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26

xiii



List of Figures

3.4 Acceleration ameas as function of vehicle speed. The black line is the
highest possible amax. The points with red circles are considered as
outliers. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27

3.5 Acceleration ameas after using the noise reduction approach. . . . . . . 27
3.6 Flow chart of the battery co-state update. The number of update is

denoted by c. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34
3.7 Flow chart of the implemented MPC-algorithm . . . . . . . . . . . . 36

4.1 Artificial driving cycle with a road length of 7km. The horizontal axis
represents the traveled distance and the vertical axis represents the
altitude. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37

4.2 Road between Alingsås and Gothenburg. The length of the driving
cycle is 40.1km. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38

4.3 The state trajectories of CV and the speed limits. The ICE-state is
not included since the engine is always on for CV. . . . . . . . . . . . 39

4.4 The control trajectories of CV and ICE limits. EM force and its limits
are not displayed since they are not available for CV. . . . . . . . . . 39

4.5 The state trajectories of HEV, including ICE-state and SOC, as func-
tion of traveled distance. The limits for SOC and speed are also
displayed. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40

4.6 The control trajectories of HEV, including EM force, as function of
traveled distance. The limits for ICE and EM are also displayed. . . . 41

4.7 The various estimated acceleration limits as function of vehicle speed.
The estimation of limits depend on the traveled distance of leading
vehicle. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42

4.8 The state trajectories of CV as function of traveled distance and the
speed limits. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43

4.9 The control trajectories of CV as function of traveled distance and
the ICE limits. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43

4.10 The time gap between the traveling times of leading vehicle and host
vehicle (CV) as function of traveled distance. . . . . . . . . . . . . . . 44

4.11 The state trajectories of HEV as function of traveled distance. The
limits for SOC and speed are also displayed. . . . . . . . . . . . . . . 45

4.12 The control trajectories of HEV as function of traveled distance. The
limits for ICE and EM are also displayed. . . . . . . . . . . . . . . . . 45

4.13 The time gap between the traveling times of leading vehicle and host
vehicle (HEV) as function of traveled distance. . . . . . . . . . . . . . 46

4.14 The actual and predicted speed of leading vehicle and its assumed
desired speed when the prediction is done once for the entire road. . . 48

4.15 Time gaps for different lengths of prediction horizon as function of
traveled distance for CV. Note that the rest of the gap represented
by the black line is not displayed as it increases significantly over
traveled distance. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49

4.16 Time gaps for different lengths of prediction horizon as function of
traveled distance for HEV. . . . . . . . . . . . . . . . . . . . . . . . . 49

xiv



List of Figures

4.17 The control trajectories as function of traveled distance when the
observer is not available. . . . . . . . . . . . . . . . . . . . . . . . . . 50

4.18 The time gap as function of traveled distance when the observer is
not available. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51

4.19 The predicted speed trajectory and the assumed desired speed of the
leading vehicle for each sample along with the actual speed trajectory
when observer is not available. . . . . . . . . . . . . . . . . . . . . . . 51

4.20 The predicted speed trajectory and the assumed desired speed of the
leading vehicle for each sample along with the actual speed trajectory
when observer is used. . . . . . . . . . . . . . . . . . . . . . . . . . . 52

4.21 Fuel consumption of CV and HEV for different lengths of prediction
horizon. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53

4.22 The final travel time of HEV for different horizons and for the entire
road (40.1km). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54

4.23 The fuel consumed by HEV for different horizons and for the entire
road (40.1km). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54

4.24 The final travel time of CV for different horizons and for the entire
road (40.1km). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54

4.25 The fuel consumed by CV for different horizons and for the entire
road (40.1km). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54

xv



List of Figures

xvi



List of Tables

4.1 Fuel consumption, final traveling time and tsum of CV for different
prediction horizon. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47

4.2 Fuel consumption, final traveling time and tsum of HEV for different
lengths of prediction horizon. . . . . . . . . . . . . . . . . . . . . . . 47

xvii



List of Tables

Variable Unit Description
α rad Road slope
s m Distance
t s Time
v m/s Vehicle speed
ωE rad/s ICE speed
ωM rad/s EM speed
TE Nm ICE torque
TM Nm EM torque
FE N Engine force
FM N EM force
Fbrk N Mechanical braking force
Febrk N Engine braking force
Fair N Aero dynamic drag force
PE W Engine power
PM W EM power
Pbrk W Mechanical braking power
Pebrk W Engine braking power
PTd W Total power loss
PMd W Power loss from EM
Ev J Vehicle kinetic energy
EB J Vehicle battery energy
λB kg/J Battery costate
µ g/s Fuel consumption
γ - gears
χ - ICE-state
uγ - Gear control input
uχ - ICE state control input
dLH m Distance between leading and host vehicle

xviii



1
Introduction

Transportation of freight by road plays an important role in the modern global mar-
ket. In our daily lives, products are seen everywhere which have been delivered by
trucks from various industries. From 2007 to 2016, the total yearly freight being
transported by road is approximately 75% in the EU [2] and about 70% in the US
[3]. However, the high demand for transportation of freight by road leads to both
environmental and financial issues. Despite representing a minority of vehicles on
road in the EU, heavy trucks are responsible for approximately 30% of the CO2
emissions according to the International Council on Clean Transportation [4]. Ac-
cording to OECD [5], the statistics show that the amount of pollutants emitted by
burning every gram of the heavy vehicle fuel and the effects of it are increasing.

To address this issue, one solution is to use a PCC (Predictive Cruise Control)
which uses information of the road topography and surrounding traffic to predict
the optimal speed of the truck [6]. For example, when the vehicle anticipates an
uphill on the road that lies ahead, it can start decreasing its speed before reaching
the top and then build up the speed when rolling downhill. Thus, more fuel is saved
and less energy from applying the service brake is wasted.

Despite this, energy consumed through engine brake is inevitable and service brake
may still need to be applied when traveling downhill. This solution can therefore
be further improved by using an HEV (Hybrid Electrical Vehicle) which includes
an additional power source, electric machine (EM). The HEV can use it for braking
and converting the kinetic energy into electric energy, which is stored in a battery
[7]. The stored energy can later be used for propulsion of the vehicle along with the
power from internal combustion engine. This also allows the engine to be turned
off during the periods of travel when the vehicle only relies on the electric machine,
which reduces the fuel consumption even further.

However, the control strategy of HEV is more complex compared to a conventional
one as it introduces more states and control signals which must be considered. The
additional states include the battery energy and the state of engine (either on or
off) and the additional control signals include the power from the electric machine
and the input for deciding whether the engine should be on or off.

1



1. Introduction

1.1 Background

There are several works related to energy optimization of conventional vehicle as well
as HEV. One of the earlier projects worked on optimizing a heavy diesel truck with
DP (Dynamic Programming) and MPC (Model Predictive Control) [8]. However,
the downside with DP is that the computation time grows exponentially with the
number of states and control signals [9]. This may be a problem for an HEV as more
states and control signals must be considered compared to a conventional one.

In the project presented in [10], a control strategy for a hybrid long-haul truck was
examined. In that project, an MPC was developed which consisted of three lay-
ers. The first layer optimized the energy of the two power sources in the vehicle
by quadratic programming method. The second layer is solved by dynamic pro-
gramming method where the integer states such as gear and the state of internal
combustion engine were optimized. The obtained control signals and states were
used for the current instance in the third layer. Their results showed that up to 4%
of fuel could be saved while allowing the vehicle speed to vary around ± 5 km/h by
minimizing the service braking.

Another work was a master thesis which presented the optimal control strategy
for multiple HEVs traveling in platoon [11]. Their control strategy was a predic-
tive CACC (Cooperative Adaptive Cruise Control) which utilized road information
to optimize the vehicle speed and reduce the fuel consumption of the vehicle pla-
toon. Their optimization problem was divided into smaller subproblems, which were
solved in two layers. The first layer was the energy management which used convex
optimization method and the second layer was the power management which used
dynamic programming method. With their implemented control algorithm, their
result showed that the average fuel consumption for each vehicle could be reduced
by 10% with a platoon of four HEVs compared to a single HEV.

For this thesis, the predictive cruise control strategy of an HEV driving on a hilly
terrain is further examined. However, in this project, an uncontrolled leading vehicle,
driving in front of the controlled host vehicle is also considered. Therefore, the
driving behaviour of the leading vehicle must also be predicted to ensure that the
host vehicle keeps a safe distance to it.

Prediction of a leading vehicle by using MPC has previously been investigated in
[12]. In their work, based on driving data obtained by experiments on an urban
road with traffic signals, a prediction model of leading vehicle was created which
estimated its acceleration/deceleration. By using the information of the predicted
driving behaviour of the leading vehicle and the traffic states, their control algorithm
could find optimal control input for the host vehicle while still keeping a safe distance
to the leading vehicle.

However, when driving on a hilly terrain, the heavy-duty leading vehicle may drop
speed due to its power limit. Therefore, an observer needs to be developed in this
thesis. By collecting measurement data of the leading vehicle, the observer can then

2



1. Introduction

estimate the power limit of the leading vehicle which is used to determine its speed
trajectory ahead.

1.2 Purpose

For this project, an MPC algorithm is developed to decrease the energy consump-
tion of the controlled vehicle while ensuring a safe distance is kept to leading vehicle
ahead. As it is assumed that there is no vehicle-to-vehicle communication, an ob-
server needs to be developed which can estimate parameters such as mass and power
to mass ratio of the leading vehicle to predict its driving behaviour.

1.3 Objective

The objective of this thesis is to develop an MPC algorithm to minimize the fuel
consumption by using an already existing control algorithm as starting point for the
development of MPC. The work is divided into the following main tasks:

• Design and implement an observer for the host vehicle in order to predict the
behaviour of a leading vehicle, including its velocity trajectory.

• Implement an MPC algorithm.

• Evaluate the performance of the MPC algorithm.

1.4 Delimitations

Only one leading vehicle in front of the host vehicle is present in driving scenarios
and perfect weather condition is assumed. Other traffic or obstacles are therefore
not taken into consideration. The optimisation is only carried out on acceleration
and braking. Therefore the steering of host vehicle is not taken into account. The
computation time of the control algorithm is not considered.

1.5 Report outline

The report starts by describing the necessary theory in Chapter 2, which includes
an overview of MPC and the physical model of the vehicle. In Chapter 3, the design
of observer, problem formulation and control strategy are explained. In Chapter 4,
the results obtained in the thesis are presented, which are discussed in Chapter 5.
The report ends with the conclusion in Chapter 6.

3



1. Introduction

4



2
Theory

In this chapter, the necessary theories to understand the thesis are presented. The
basic concept of MPC is explained. The vehicle model is introduced as well.

2.1 Concept of MPC

MPC is a control method that has been applied in industries since late 70s [13]. It
is also known as receding horizon control as its concept is based on the receding
horizon idea. Unlike most controllers, MPC can effectively handle systems with
multiple inputs and outputs which might be depended on each other [14]. Another
big advantage with MPC is that constraints can be put for the control signals and
the states.

Figure 2.1: Simple block diagram of MPC.

The procedure of MPC shown in Figure 2.1 can be summarized by the following
steps [14][15]:

1. At current sample instance k, the output signals y(k) are predicted with the
process model for N instances ahead. The predicted output signals depend on
the future control sequence over control horizon M .

2. Based on formulated cost function, objective and constraints for an optimiza-
tion problem, the optimal control sequence is obtained and chosen.

3. The first element of the optimal control sequence is applied, and the rest is
discarded. The controller then moves to next instance (k + 1) and returns to

5



2. Theory

step 1 to repeat the procedure.

Normally, the length of control horizon M is set to be shorter than the length of
prediction horizon N [15]. If that is the case, the rest of the control sequence after
instance k +M is set as either u(k +M) or 0.

2.2 Convex optimization problem

A standard form of convex optimization problem can be formulated as [15][16]

minimize f(x)
s.t. gi(x) ≤ 0, i = 1, 2, ..,m

hi(x) = 0, i = 1, 2, .., p
(2.1)

where f is a cost function and x = {x1, x2, ...xn} represents the optimization vari-
ables that should minimize f . The inequality and equality constraint functions are
denoted by gi and hi, respectively. Both f and gi are convex, and hi are affine [15].
Another important property is that the local minimum is a global optimum.

These properties described for convex optimization problem are important when
formulating our optimization problem later.

2.3 Vehicle model

Figure 2.2: The powertrain configuration of host vehicle which shows gear box,
final drive, ICE (Internal Combustion Engine), EM (Electric Machine) and their
power sources. ICE and EM are connected to same gears.

The vehicle is modelled as a point mass that has the powertrain as illustrated in
Figure 2.2, which is based on the HEV powertrain used in previous work by De-

6



2. Theory

partment of Electrical Engineering at Chalmers University of Technology and Volvo
Group Trucks Technology [10]. The powertrain is equipped with an ICE (Internal
Combustion Engine) and an EM (Electrical Machine) which are connected to the
same gear box and powered by fuel and battery, respectively. The clutch is respon-
sible of switching between the EM and ICE. The vehicle model has three continuous
states which are speed v, traveling distance s and battery energy EB. The model
also involves two real valued discrete states, which are the ICE state χ and gear
number γ. Thus, the model is a hybrid system with mixed real- and integer states
and control signals.

The longitudinal vehicle dynamic is modelled as

mv̇(t) = FD(t)−mg sin(α)− Fair(v)− Frol(α) (2.2)

where m is the mass of the host vehicle. The total traction force delivered to the
wheels by ICE and EM is denoted by FD(t). The gravitational force is denoted by
g and α is the slope of the road depended on the travel distance s(t), which in turn
is depended on the travel time t. The force from the rolling resistance Frol and air
resistance Fair are described by

Frol(α) = mgcrcos(α) (2.3)

Fair(v) = ρaAfcd

2 v2(t) (2.4)

where cr is the rolling resistance coefficient, ρa is air density, Af is frontal area of the
host vehicle and cd is the aerodynamic drag coefficient.

As shown in Figure 2.2, in this parallel configuration the EM and/or ICE transmits
mechanical power to wheels. This mechanical power balance is described as

PE(t) + PM(t) + Pbrk(t) + PEbrk(t) = FD(t)v(t) + PTd(γ, χ, PE, PM, µγ, µχ) (2.5)

where PTd(t) includes power loss due to shifts of gear and ICE and transmission
losses. The braking powers Pbrk and PEbrk represent the power consumed from
mechanical brake and engine brake, respectively. The power used for propulsion
from ICE is denoted by PE(t), while the power from EM is denoted by PM(t).

The electrical power balance is described as

PB(t) = PM(t) + PMd(v, PM) + PBd(PB) + PA(t) (2.6)
where PB(t) is internal battery power, PMd(v, PM) and PBd(PB) are power loss from
EM and battery, respectively. The power consumed by auxiliary devices is denoted
by PA(t), but it is neglected for this HEV model.

The states of gear and ICE are defined as γ and χ, respectively, which can have the
following values

7



2. Theory

γ ∈ {1, ..., γmax}, χ ∈ {0, 1} (2.7)
The values χ can have means it is either off (0) or on (1).

Their states for next time instance (γ+, χ+) are described by

γ+ = γ + µγ, χ+ = χ+ µχ (2.8)

where µγ ∈ {−1, 0, 1} and µχ ∈ {−1, 0, 1} are the switch commands for gear and
state of ICE, respectively. When the gear is switched or the state of ICE is changed,
additional fuel will be consumed, which are defined as the cost terms Wγ and Wχ,
respectively.

2.3.1 ICE model

The fuel consumption of ICE, denoted by µ, as the function of engine speed and
torque is formulated as

µ(ωE(t), TE(t)) = a0+a1ωE(t)+a2ω
3
E(t)+a3ω

5
E(t)+a4ωE(t)TE(t)+a5ωE(t)T 2

E(t) (2.9)

where a0−5 are constants used for fitting. By fitting the model with measurements,
the best fitted model is to put a1 and a2 as 0. Figure 2.3 illustrates the fuel con-
sumption of ICE for different engine speeds and how well the model fits the mea-
surements.

0 100 200 300 400 500 600 700

Torque (Nm)

1

2

3

4

5

6

7

8

F
u

e
l 
C

o
n

s
u

m
p

ti
o

n
 (

g
/s

)

800

1000

1000

1200

1200

1200

1400

1400

1400

1600

1600

1600

1800

1800

1800

20
00

2000

2000

800

1000

1000

1200

1200

1200

1400

1400

1400

1600

1600

1600

1800

1800

1800

2000

2000

2000

Measurements, speed (rpm)

Approximated model, speed (rpm)

Figure 2.3: Fuel consumption is shown as the function of torque for various engine
speeds. The measurements are shown in black and the fitted model is shown as
contour. The numbers on the graphs represent the engine speed.

8



2. Theory

The speed and torque of ICE, denoted by ωE(t) and TE(t) respectively, are described
by

ω(t) = v(t)r(γ) (2.10a)

TE(t) =


FICE(t)
r(γ)η , if FICE(t) ≥ 0
FICE(t)η
r(γ) , if FICE(t) < 0

⇔ TE(t) = 1
r(γ)max

{
FICE(t)
η

, ηFICE(t)
}

(2.10b)

where η is the transmission efficiency from engine to wheel and FICE is the force
delivered by ICE which can either be used for propulsion (FICE ≥ 0) or braking
(FICE < 0). ICE ratio, denoted by r(γ), is defined as

r(γ) = rg(γ)rf

Rw
(2.11)

where Rw is the radius of the wheels and rg is the gear ratio. The gear ratio of the
differential gears between ICE and EM is denoted by rf.

The torque limits of ICE are illustrated in Figure 2.4, where they are plotted as a
function of engine speed with the efficiency. The Figure also includes the maximum
power that ICE can deliver.

800 1000 1200 1400 1600 1800 2000 2200 2400 2600

Speed (rpm)

-600

-400

-200

0

200

400

600

800

T
o

rq
u

e
 (

N
m

)

10 1015 1520 2025 2530
3035

35

36

36

37

37

38

38

38

39

3
9

40

4
04

1

41

4
2

Measurements

Effieciency [%]

Fitted torque limits

Power limit

Figure 2.4: Torque limits and efficiency contour of ICE are shown as the function
of engine speed. The original torque limits are in black and fitted torque limits are
in red. The green line represents the maximum power delivered by ICE.

Converting engine speed and torque from Figure 2.4 to vehicle speed and force gives
Figure 2.5 which illustrates the longitudinal force delivered by the engine to the
wheels plotted as function of vehicle speed for different gear numbers.

9



2. Theory

20 40 60 80 100 120 140 160 180 200 220

Speed[km/h]

-100

-80

-60

-40

-20

0

20

40

60

80

100

F
o

rc
e

[k
N

]

2
3

4
5

6 7

8 9 10 11 12

2

3
4

5
6 7 8 9 10 11 12

Force per gear

Force limits

Figure 2.5: Longitudinal force that engine can deliver as function of vehicle speed
for different gears.

From now on, the propulsion (FICE ≥ 0) and braking force (FICE < 0) from ICE are
referred as FE and FEbrk, respectively.

The limit of FE(t) can be described by several constraints. The first one is estimated
as function of vehicle speed which is formulated as

FE(t) ≤
(
b1 + b2v

2(t)r2(γ)
)
r(γ)η (2.12)

where b1 and b2 are constant coefficients. The second one is that FE(t) should not
exceed the maximum engine torque b0

FE(t) ≤ b0r(γ)η (2.13)

The propulsion force is also limited by the maximum engine power PEmax

FE(t) ≤ ηPEmax

v(t) (2.14)

However, the limit for FE, as shown in Figure 2.5, can be estimated by

FEmax(t) = F0 + PEmax

v(t) (2.15)

where F0 is a constant used for fitting the limit. This limit can be used to determine
whether the host vehicle is able to reach up to a certain desired speed or not. This

10



2. Theory

is useful when predicting the speed trajectories of leading vehicle and host vehicle,
which will be later described in Chapter 3.

The last constraint is that FE(t) cannot be negative

FE(t) ≥ 0 (2.16)

The engine braking force FEbrk has two constraints. The first one is formulated as
function of v(t)

FEbrk ≥
(
c1 + c2v(t)2r(γ)2

) r(γ)
η

(2.17)

where c1 and c2 are constants used to fit the model. The last one is that FEbrk
cannot be positive

FEbrk ≤ 0 (2.18)

Multiplying (2.12)-(2.16) and (2.17)-(2.18) with v(t) yields the expressions of con-
straints in terms of power, which can also be further simplified as

PE(t) ≤ ηPEmax (2.19a)

PE(t) ∈
[
0,min

{
b0, b1 + b2r

2(γ)v2(t)
}]
r(γ)ηv(t) (2.19b)

PEbrk(t) ∈
[(
c1 + c2v(t)2r(γ)2

)
, 0
] r(γ)

η
v(t) (2.19c)

2.3.2 EM model

Since ICE and EM are connected to the same gear box, they share the same gearing
ratio (r). This also means that EM has the same speed as ICE (w).

The expression of the torque of EM, denoted by TM(t), depends on whether EM is
used for propulsion or generation as described by

TM(t) =


FM(t)
r(γ)η , if FM(t) ≥ 0
FM(t)η
r(γ) , if FM(t) < 0

⇔ TM(t) = 1
r(γ)max

{
FM(t)
η

, ηFM(t)
}

(2.20)

where FM is the force delivered by EM to the wheels. Torque limits are shown as
the function of EM speed in Figure 2.6.

11



2. Theory

0 500 1000 1500 2000 2500 3000

Speed [rpm]

-1500

-1000

-500

0

500

1000

1500

T
o

rq
u

e
 [

N
m

]

6060
60

6
0

60 60
7575

75
7

5
75 75

8282
82

8
2

82 82

8686
8
6

8
6

86
86

8888
8
8

8
8

88
88

8989
8
9

8
9

89
89

9090
9
0

9
0

90
90

9191
9
1

9
1

91

91

9292
9
2

9
2

92

92

9393
9
3

9
3

93

93

9494

9
4

9
4

94
94

95
95

9
5

95 95

96

9
6

96

Measurements

Efficiency [%]

Fitted torque limits

Figure 2.6: Torque limits as function of EM speed. The efficiency percentage is
shown as contour, original torque limits are in black and fitted torque limits are in
red.

The black lines represent the torque limits which are fitted by

TMmax = min
{
d1, d2 + d3

ω(t)

}
(2.21a)

TMmin = max
{
e1, e2 + e3

ω(t)

}
(2.21b)

where d1, d2, d3, e1, e2 and e3 are constants used for fitting. The limits of FM are
then expressed as

FMmax(t) = min
{
d1, d2 + d3

v(t)r(γ)

}
r(γ)η (2.22a)

FMmin(t) = max
{
e1, e2 + e3

v(t)r(γ)

}
r(γ)
η

(2.22b)

Multiplying Equation (2.22) with v(t) gives the expression of EM limits in terms of
power

PMmax = min
{
d1, d2 + d3

v(t)r(γ)

}
r(γ)ηv(t) (2.23a)

PMmin = max
{
e1, e2 + e3

v(t)r(γ)

}
r(γ)v(t)

η
(2.23b)

12



2. Theory

The power losses of EM shown in Figure 2.7 is modelled as

PMd(t) = h1ω(t) + h2ω
3(t) + h3ω(t)|TM(t)| (2.24)

where h1, h2 and h3 are constants for fitted model.

-1500 -1000 -500 0 500 1000 1500

Torque [Nm]

-150

-100

-50

0

50

100

150

E
l.
 p

o
w

e
r 

[k
W

]

500

500

500

1000

1000

1000

15
00

15
00

20
00

20
00

2
5
0
0

2
5
0
0

3
0
0
0

3
0
0
0

500

500

500

1000

1000

1000

15
00

15
00

20
00

20
00

2
5
0
0

2
5
0
0

3
0
0
0

3
0
0
0

Measurements, speed (rpm)

Fitted model, speed (rpm)

Figure 2.7: Electrical power consumed by EM is shown as the function of torque
for various EM speeds. The original model is shown in black and the fitted model
is shown as contour.

The total power consumed by EM is the sum of PMd and PM.

2.3.3 Battery model

Battery energy EB(t) is regulated by the state

ĖB(t) = −PB(t) (2.25)

The state of charge, denoted by SOC, is defined according to Equation

SOC(t) = EB(t)
EBmax

(2.26)

where EBmax is the maximum energy capacity of the battery. The battery energy is
limited by

13



2. Theory

EB(t) ∈ [SOCmin, SOCmax]EBmax (2.27)
where SOCmin and SOCmax are lower and upper bounds of SOC, respectively. The
power loss of battery, denoted by PBd, is expressed as

PBd(t) = R

V 2
oc
P 2

B(t) (2.28)

where Voc represents constant open circuit voltage of the battery and R represents
its constant resistance.

2.3.4 Safety constraint

A typical scenario of host vehicle driving on a road with leading vehicle in front of
it can be seen in Figure 2.8 where there are both up and downhills.

Figure 2.8: The leading vehicle and host vehicle driving on road with hills which
is 7km long.

A safety constraint needs to be introduced to ensure that a safe distance can be kept
between the host and leading vehicle. This can be formulated with their respective
traveling times and add a time headway as described by

t ≥ tL + ∆t (2.29)

where tL and ∆t denote the traveling time of leading vehicle and the time headway,
respectively. The safety constraint can also be formulated in traveling distance as
described by

dLH = sL(t)− s(t) ≥ ∆d (2.30)

14



2. Theory

where sL and s are the longitudinal positions of the leading and host vehicle, re-
spectively. Thus, dLH is the distance between the vehicles and ∆d is the minimum
required distance between them.

2.3.5 Aerodynamic drag model

Having a leading vehicle in front leads to an aerodynamic drag reduction of force
for the host vehicle. The reduction depends on the distance between the vehicles,
their respective speeds and geometries.

The aerodynamic drag reduction is modelled as follows,

Fair(v, dLH) = F 0
air(v(t)) (1− fd(dLH(t))) (2.31a)

where F 0
air is the air resistance force experienced by host vehicle if there is no leading

vehicle ahead. The air resistance force in turn is described by

F 0
air(v) = ρaAfcd

2 v(t) (2.31b)

The expression of aerodynamic drag coefficient for host vehicle, denoted by fd(dLH),
is described by

fd(dLH) = a1LHexp(−b1LHdLH(t)) + a2LHexp(−b2LHdLH(t)) (2.32)

where the coefficients a1LH, a2LH, b1LH and b2LH are adjusted by fitting measurement
data. Figure 2.9 illustrates the drag reduction of host vehicle where there is one
leading vehicle present. The aerodynamic drag model described by Equation (2.32)
fits the measurement data in Figure 2.9. It can be seen that the longer the distance
between the vehicles is, the less air drag reduction fd there is.

0 10 20 30 40 50 60

vehicle to vehicle distance [m]

0.1

0.2

0.3

0.4

0.5

0.6

A
ir
 d

ra
g

 r
e

d
u

c
ti
o

n

Measurement

Fitted model

Figure 2.9: Comparison between measurement data and fitted model of aerody-
namic drag reduction fd(dLH).

15



2. Theory

16



3
Methods

This chapter describes the procedure for predicting the behaviour of leading ve-
hicle and the control strategy used to optimize the fuel consumption of the host
vehicle.

3.1 Overview

The controller is a PCC (Predictive Cruise Controller), which estimates the optimal
trajectories [17][18][19] for the states and control signals of the host vehicle in order
to minimize its fuel consumption. For this project, the controller is extended to
an MPC where the control horizon M is set as the same length as the prediction
horizon N . At current time instance t0, the optimal trajectories are predicted N
instances ahead. Thus, the final instance of the predicted horizon becomes

tf = t0 +N (3.1)

The states are the speed v, traveled distance s, battery energy EB, gear γ and ICE
state χ. The control signals are the powers PM, PE PEbrk, Pbrk, gear selection uγ
and ICE selection uχ. A constant cruising speed v̄ is assumed to be set for the host
vehicle.

However, when the road topography and the behaviour of leading vehicle are taken
into consideration, it might not be possible to maintain the set cruising speed for
certain instances. To predict how the leading vehicle drives, some of its parameters
need to be estimated first, including its power to mass-ratio, by a leading vehicle
observer. The estimated parameters can then be used to determine if the cruising
speed of leading vehicle, denoted by v̄L, is feasible or not (more on this in Section
3.6.1). Based on the road topography and the predicted driving of leading vehicle,
a reference speed trajectory of host vehicle can then be obtained.

With the reference speed trajectory and a formulated optimization problem, the
controller estimates the optimal trajectories for the states and control signals of host
vehicle, while ensuring a safe distance to the leading vehicle is kept. Only the first

17



3. Methods

elements of the respective trajectories are applied. The rest is then discarded and
MPC performs an update with the whole procedure repeated at next instance.

3.2 Formulation of optimization problem

The optimization problem that the controller should solve is formulated as

minimize J =
∫ tf

t0
(χ(t)µ(·) +Wγ(·) +Wχ(·))dt

subject to
(3.2a)

PE(t) + PM(t) + Pbrk(t) + PEbrk(t) = FD(t)v(t) + PTd(·) (3.2b)

PB(t) = PM(t) + PMd(v, PM) + PBd(PB) (3.2c)

mv̇(t) = FD(t)− Fair(v, dLH)−mg(sin(α) + crcos(α)) (3.2d)

ĖB(t) = −PB(t) (3.2e)

s(t0) = s0, s(tf) = sf (3.2f)

ṡ(t) = v(t) (3.2g)

v(t0) = v0 (3.2h)

v(t) ∈ [vmin(t), vmax(t)] (3.2i)

t ∈ [t0, tf] (3.2j)

tf − t0 ≤ tmax (3.2k)

PE(t) ≤ ηPEmax (3.2l)

PE(t) ∈
[
0,min

{
b0, b1 + b2r

2(γ)v2(t)
}]
r(γ)ηv(t) (3.2m)

PM(t) ∈ [PMmin(v, γ), PMmax(v, γ)] (3.2n)

Pbrk(t) ≤ 0 (3.2o)

PEbrk(t) ∈
[(
c1 + c2v(t)2r(γ)2

)
, 0
] r(γ)

η
v(t) (3.2p)

EB(t0) = EB0, EB(tf) ≥ EBf (3.2q)

EB(t) ∈ [SOCmin, SOCmax]EBmax (3.2r)

χ+(t) = χ(t) + uχ(t), χ(t) ∈ X, uχ(t) ∈ Uχ (3.2s)

γ+(t) = γ(t) + uγ(t), γ(t) ∈ Γ, uγ(t) ∈ Uγ (3.2t)

sL(t) ≥ s(t) + ∆d (3.2u)

The terms Wγ and Wχ are the penalties added for changing gear-and ICE-state,
respectively. This is to avoid shifting too frequently, as it is not desirable. Note

18



3. Methods

that µ is multiplied with χ to ensure that fuel consumption only occurs when ICE
is on.

Since the constant efficiency η already includes the losses from the transmission,
only the losses from shifting gear and ICE-state are included in PTd.

This optimization problem has both real valued and integer states and variables,
making it computationally heavy to solve. Therefore, the problem is divided into
two layers, which will be later described in Section 3.3.

Equation (3.2k) ensures that even if v deviates from the reference speed vr, the host
vehicle should still be able to complete the horizon within the same time frame tmax
as if it would have driven with vr.

3.3 Control scheme

The optimization problem in Equation (3.2) is solved by two layers, which is illus-
trated in Figure 3.1. This is a common method, which has been done in previous
works [20][21][9]. Both layers minimize the cost function given in Equation (3.2a),
but with different methods and in regards to different states/control signals. The top
and bottom layer are referred as energy and power management, respectively.

Figure 3.1: The control scheme divided into two layers, energy and power manage-
ment. Energy management estimates the optimal trajectories for v and λB, which
are then sent to the power management. The power management in turn estimates
the optimal trajectories for γ and χ, which are then sent to energy management to
estimate its optimal state and control trajectories again.

19



3. Methods

After obtaining the reference speed trajectory vr, the energy management solves the
optimization problem with convex optimization to estimate the optimal trajectories
for the states v, t and EB as well as the control signals PE, PM, PEbrk and Pbrk.
The energy management also estimates the battery costate trajectory λB, which
will be further described in Section 3.8. Both v and λB are then sent to the power
management.

The power management estimates the optimal trajectories for the states EB,γ and
χ as well for the control signals, including gear selection uγ and ICE-selection uχ,
by using dynamic programming. The energy management then receives γ and χ
to solve the optimization problem and send v and λB to the power management
again.

This process is repeated until a solution converges or until a maximum number of
iteration has been reached.

3.4 Variable change

As data of road topography are usually given in space coordinates, it is more bene-
ficial to work in space domain than in time domain. Therefore, the travel distance s
replaces the travel time t as the independent variable. Rewriting from time domain
to space domain should be done according to

t′(s) = dt

ds
= 1
v(s) (3.3)

In space domain, it is easier to work with forces and kinetic energy instead of power
and velocity. Therefore, the forces are given as

FE = PE(s)
v(s) , FM = PM(s)

v(s) , FB = PB(s)
v(s) , Fbrk = Pbrk(s)

v(s) , FEbrk = PEbrk(s)
v(s) (3.4)

and the speed v(s) is replaced with kinetic energy Ev(s) according to

Ev(s) = mv2(s)
2 (3.5)

With the variable change, the equation of motion from (2.2) is rewritten as

E ′v(s) = mv′(s)v(s) (3.6)

The final instance for the predicted horizon described in Equation (3.1) is also
modified as

sf = s0 + Sp (3.7)

20



3. Methods

where s0 and Sp are the current instance and prediction horizon in space domain,
respectively.

3.5 Linearization and approximations

By changing the variables, the constraints which had 1/v(s) will instead have 1/
√
Ev(s),

as seen in the function ft(Ev) described by

ft(Ev) = 1
v(s) =

√
m

2Ev(s) (3.8)

where t denotes the expression in Equation (3.3). However, as those constraints
are not convex, this is an issue for the energy management which uses convex op-
timization to solve the optimization problem. Therefore, the function needs to be
linearized around the reference kinetic energy Êv(s), which is the kinetic energy
when the host vehicle drives with reference speed vr. The linearization is described
as

f lin
t (Ev) = ft(Êv(s)) + ∂ft

∂Ev

∣∣∣∣∣
Êv

∆Ev(s) (3.9)

where ∆Ev(s) = Ev(s)− Êv(s).

3.5.1 ICE model

The fuel consumption µ is modified as

µ̃(·) = µ(·)
v(s) (3.10)

In the beginning of each MPC-update, the gear trajectory has not been updated
before solving the optimization problem in energy management (more details de-
scribed in Section 3.3). This might lead to infeasible force delivered by ICE, as
the current gear trajectory may not have been properly selected to provide suffi-
cient force to reach up to the updated speed v. Therefore, FE is reformulated and
expressed as

FE(s) = χ(s)FE1(s) + FE2(s) (3.11)

21



3. Methods

where FE1 is the force from current gear trajectory and FE2 is an abstract force
which can be delivered from any other chosen gear and state of ICE. The ICE-state
χ is multiplied with FE1 to ensure that the force is only available when ICE is on.
If FE1 is not sufficient to fulfill the constraint in Equation (2.12), FE2 is applied to
cover up the rest of FE.

The constraint for FE from (2.12) is subsequently reformulated as

χFE1(s) + FE2(s) ≤ ηPEmax

√
m

2Ev(s) (3.12)

This however needs to be linearized as

χFE1(s) + FE2(s) ≤ ηPEmaxf
lin
t (Ev(s)) (3.13)

The constraint for FE1 is now described by Equation

FE1(s) ∈
[
0,min

{
b0, b1 + 2b2

m
Ev(s)r2(γ)

}]
r(γ)η (3.14)

The constraint for braking force FEbrk is also reformulated as

FEbrk(s) ∈
[(
c1 + 2c2

m
Ev(s)r2(γ)

)
, 0
]
r(γ)
η

(3.15)

3.5.2 EM model

The wheel force from EM has the constraints described by

FMmax(Ev) = min
{
d1, d2 + d3

r(γ)

√
m

2Ev(s)

}
r(γ)η (3.16a)

FMmin(Ev) = max
{
e1, e2 + e3

r(γ)

√
m

2Ev(s)

}
r(γ)
η

(3.16b)

However, these Equations are not convex. Therefore, they are linearized as described
by Equation (3.9), which gives

FMmax(Ev) = min
{
d1, d2 + d3

r(γ)f
lin
t (Ev(s))

}
r(γ)η (3.17a)

FMmin(Ev) = max
{
e1, e2 + e3

r(γ)f
lin
t (Ev(s))

}
r(γ)
η

(3.17b)

22



3. Methods

The force losses from EM, denoted by FMd, is described by

FMd(s) = h1r(γ) + 2h2r
3(γ)
m

Ev(s) + h3

∣∣∣∣∣max
{
FM(s)
η

, ηFM(s)
}∣∣∣∣∣ (3.18)

3.5.3 Battery model

The energy battery is reformulated as

E ′B(s) = −FB(s) (3.19)

Force dissipation from battery, denoted by FBd(s), is described by

FBd(s) = R

V 2
oc

√
2Ev(s)
m

F 2
B(s) ≈ R

V 2
oc

√
2Êv(s)
m

F 2
B(s) (3.20)

As seen in the Equation, the expression is simplified by replacing Ev(s) with Êv(s).
This is to avoid multiplication of different variables, which would otherwise have
made it into a non-convex optimization problem.

3.5.4 Aerodynamic drag model

The air resistance force Fair in Equation (2.31a) is rewritten in space domain as

Fair(Ev, dLH) = F 0
air(Ev(s)) (1− fd(dLH(s))) (3.21)

The function fd(dLH(s)) is however both nonlinear and non-convex. Therefore, it is
linearized around the distance between the vehicles estimated with their reference
speeds, denoted by d̂LH(s)), as seen in

F lin
air (Ev, dLH) = caEv(s)

(
1− fd(d̂LH(s))

)
− caÊv(s)

(
dLH(s)− d̂LH(s))

) ∂fd

∂dLH

∣∣∣∣∣
d̂LH
(3.22)

The distance between leading and host vehicle, denoted by dLH, is calculated as

dLH(s) = xL(s)− x(s) (3.23)

where xL(s)and x(s) are the longitudinal positions of leading and host vehicles,
respectively, as function of s. By assigning x(s) = s, the leading vehicle position
can be given as

x
′

L(s) = vL(s)
v(s) (3.24)

23



3. Methods

Assuming that leading vehicle speed vL(s) does not deviate much from its desired
speed v̄L, Equation (3.24) is simplified as

x
′

L(s) = v̄Lt
′(s) (3.25)

By integrating Equation (3.25), xL can then be described by Equation

xL(s) = v̄L(t(s)− t0) (3.26)

Equation (3.23) can therefore be rewritten as

dLH(s) = v̄L(t(s)− t0)− s (3.27)

3.6 Reference speed of host vehicle

Before solving the optimization problem, a reference speed trajectory of the host
vehicle, vr, needs to be obtained. In this section, the process for predicting vr is
described. Only the force delivered by ICE is considered to make the comparison of
host vehicle as CV (Conventional Vehicle) and as HEV more fair.

3.6.1 Leading vehicle observer

The importance of maximum engine power was previously described in Section 2.3.1.
However based on the equation of motion, another term is also unknown which is
the ratio of aerodynamic drag and mass. Therefore, rather than the maximum
longitudinal force FLmax, the limit that needs to be estimated is the acceleration
limit amax described by

amax = FLmax − FLair

mL
= FL0

mL
+ PLmax

mL · vL(s) −
cLa · v2

L(s)
2mL

(3.28)

where mL is the mass of leading vehicle, FL0 is a constant force parameter to fit the
limit, cLa is its aerodynamic drag coefficient and PLmax is its maximum engine power.
Thus, the scalar parameters that need to be obtained are l0 = FL0

mL
, l1 = PLmax

mL
and

l2 = cLa
2mL

. With the measurement data (including traveling time, speed of leading
vehicle as well as the slope of the road topography), the measured acceleration
capabilities ameas can be calculated according to

ameas = FL

mL
− ca · v2

L(s)
2mL

= v̇L(s) + g · (sinα + crcosα) (3.29)

24



3. Methods

To illustrate ameas, an example is shown in Figure 3.2. In this Figure, ameas have
been calculated by using measurement data collected with sample distance of 80m
from a vehicle which has traveled for 20km.

60 65 70 75 80

Vehicle speed[km/h]

0.02

0.04

0.06

0.08

0.1

0.12

0.14

0.16

0.18

0.2

0.22

A
c
c
e

le
ra

ti
o

n
[m

/s
2
]

a
meas

Speed-clusters

Figure 3.2: Acceleration as function of vehicle speed. The blue star points repre-
sent ameas and the black lines represent the speed-clusters.

Since the ameas-values which operate on amax are relevant for estimating amax, only
the highest values of ameas are needed. Therefore, ameas are grouped based on their
speeds by several shorter but equally long intervals referred as speed-clusters. In
Figure 3.2, the number of speed-clusters is seven.

For each speed-cluster, the highest ameas-value is then saved and the rest is discarded.
The limit amax can then be estimated by solving LP (Linear Programming) [22] with
the cost function formulated as

min
l0,l1,l2

∫ vLmax

0
aLmax(vL)dvL =

K∑
j=1

amax(vLj) = l0 ·K + l1
K∑
j=1

1
vLj
− l2

K∑
j=1

vLj
2

s.t. amax(vLj) ≥ ameasj
, j = 1, 2, .., K

(3.30)

where vLmax denotes the highest measured vehicle speed collected and K denotes
the number of relevant points. From what has been previously been studied, amax
should be a monotonically decreasing function. Therefore, boundaries for l0,l1 and
l2 are put to ensure that the estimated amax does not get an unexpected shape such
as concave function.

After the vehicle parameters l0, l1 and l2 have been obtained from the observer, they
can then be used to estimate amax as described by Equation (3.28). The estimated
amax is seen in Figure 3.3.

25



3. Methods

60 65 70 75 80

Vehicle speed[km/h]

0.02

0.04

0.06

0.08

0.1

0.12

0.14

0.16

0.18

0.2

0.22

A
c
c
e
le

ra
ti
o
n
[m

/s
2
]

a
meas

Estimated a
max

Speed-clusters

Figure 3.3: Acceleration as function of vehicle speed. The blue star points repre-
sent ameas.

3.6.2 Noise disturbance

For the example described in Figures 3.2 and 3.3, simulated measurements with-
out noise disturbance were used. However, real measurement data contains noise
disturbance which can severely affect the results.

To reduce the impact of it, some measures need to be taken. The measured speed
is first smoothed with Savitzky-Golay filter [23] before ameas are calculated. A limit
for ameas as function of vehicle speed is also introduced in observer to further reduce
the noise. If an ameas exceeds this limit, it will be removed and not be considered
when amax is estimated. In the observer, a limit for jerk (derivative of acceleration
in regards to time) is also put to ensure that one ameas-point does not deviate too
much from other points.

Figure 3.4 shows an example of ameas-points collected as function of vehicle speed
and where there are points which deviate significantly from the rest, which are
considered as outliers. The black line represents the highest possible amax. In this
example, there are three ameas-points which lie above that limit. There is also
another ameas-point which lies just below the limit but deviates significantly from
the other points.

26



3. Methods

20 30 40 50 60 70 80 90

Vehicle speed[km/h]

0

5

10

15

A
c
c
e
le

ra
ti
o
n
s
[m

/s
2
]

a
meas

outliers

Highest possible a
max

Figure 3.4: Acceleration ameas as function of vehicle speed. The black line is the
highest possible amax. The points with red circles are considered as outliers.

With the approach to reduce noise impact, the three points above the limit are
neglected. The point just below it is solved with the limit put for jerk. Figure 3.5
shows the result of filtering out the outliers.

20 30 40 50 60 70 80 90

Vehicle speed[km/h]

0

5

10

15

A
c
c
e
le

ra
ti
o
n
s
[m

/s
2
]

a
meas

outliers

Highest possible a
max

Figure 3.5: Acceleration ameas after using the noise reduction approach.

27



3. Methods

3.6.3 Leading vehicle reference speed predictor

After the vehicle parameters l0, l1 and l2 are obtained from the observer, they can
then be used to determine if its desired speed v̄L (assumed to be known) is feasible
or not. The speed trajectory of the leading vehicle, denoted by vLr, can then be
predicted by numerically solving

vLr(s) = min
{
v̄L,

∫ sf

s0
min

{
acom

vLr(s)
,
awLmax(s)
vLr(s)

}
ds

}
(3.31)

with initial value vLr(s0) as the current speed of the leading vehicle. For comfort,
a limit for how much the vehicle can accelerate for comfortable driving is also in-
troduced, which is denoted by acom. For those instances where v̄L is not considered
feasible, the leading vehicle will drive with either acom or maximum vehicle acceler-
ation, denoted by awLmax, which is described by

awLmax(s) = amax − g · (sin(α) + crcos(α)) (3.32)

With the predicted speed trajectory, the traveling time of leading vehicle, denoted
by tL, can be calculated which will be used for the safety constraint described by
Equation (2.29). The safety constraint will also be taken into account for prediction
of speed trajectory of the host vehicle.

3.6.4 Host vehicle reference speed predictor

Prediction of speed trajectory of the host vehicle is similar to the case for the leading
vehicle as described by Equation (3.31). For the host vehicle however, the safety
constraint with tL is also taken into consideration. Therefore, the prediction of the
reference speed trajectory of the host vehicle, vr, is calculated by

vr(s) = min
{
v̄, vsafe(s),

∫ sf

s0
min

{
acom

vr(s)
,
awmax(s)
vr(s)

}
ds

}
(3.33)

where the initial value vr(s0 = 0) = v̄ and for the upcoming updates vr(s0 > 0) = v0
(current speed of host vehicle). The highest allowed speed of host vehicle based on
the safety constraint, which is denoted by vsafe(s), is calculated by

vsafe(s) = ds

tL(s+ 1)− tL(s) (3.34)

where ds is the sample distance. The maximum acceleration of host vehicle, denoted
by awmax, is described by

28



3. Methods

awmax(s) = F0

m
+ PEmax

mvr(s)
− cav

2
r(s)

2m − g(sin(α) + crcos(α)) (3.35)

The reference speed trajectory vr is then sent to the energy management where the
optimal state trajectories, including v, will be estimated.

3.7 Energy management

After variable change has been made as described in Section 3.4, the optimization
problem has turned convex and can finally be solved in energy management. In this
layer, the problem is reformulated as

minimize J̃ =
∫ sf

s0
(χ(s)µ̃)ds

subject to
(3.36a)

t′(s) = f lin
t (Ev(s)) (3.36b)

E ′v(s) =χ(s)FE1(s) + FE2(s) + FM(s) + Fbrk(s) + χ(s)FEbrk(s)+
+ F lin

air (Ev, dLH)−mg(sin(α) + crcos(α))
(3.36c)

E ′B(s) = −FB(s) (3.36d)

FB(s) ≥ max
{
FM(s)
η

, ηFM(s)
}

+ FMd(s) + FBd(s) (3.36e)

t(sf) ≤ tmax (3.36f)

t(s0) = t0, Ev(s0) = mv2
0

2 (3.36g)

t(s) ≥ tL(s) + ∆t (3.36h)

Ev(s) ∈ m2
[
v2

min(s), v2
max(s)

]
(3.36i)

χ(s)FE1(s) + FE2(s) ≤ ηPEmaxf
lin
t (Ev(s)) (3.36j)

FE1(s) ∈ ηr(γ)
[
0,min

{
b0, b1 + 2b2r

2(γ)
m

Ev(s)
}]

(3.36k)

FEbrk ∈
[(
c1 + 2c2

m
Ev(s)r2(γ)

)
, 0
]
r(γ)
η

(3.36l)

Fbrk(s) ≤ 0, FE2(s) ≥ 0 (3.36m)

FM(s) ∈
[
FMmin(Ev), FMmax(Ev)

]
(3.36n)

EB(s0) = EB0, EB(sf) ≥ EBf (3.36o)

EB(s) ∈
[
SOCmin, SOCmax

]
EBmax (3.36p)

29



3. Methods

There are three states t, Ev and EB, and six control signals FE1, FE2, FM, FB, Fbrk
and FEbrk. Note that integer states, such as γ and χ, as well as the penalty terms
in Equation (3.2a) have been removed in this layer. There are several options for
solving this convex problem. In this project, the problem is solved by quadratic
programming [24].

After the optimization problem has been solved, the estimated trajectories for the
speed v and battery costate λB are then sent to the power management. The control
trajectories are also sent to obtain the demanded force FD (more on this in Section
3.8.1).

3.8 Power management

Since power management has received the battery costate and optimal speed trajec-
tory, constraints for v and travel time t in the optimization problem can be removed.
The problem is thus reformulated as

minimize J =
∫ sf

s0
(χµ(FE, γ) +Qtot)ds

subject to
(3.37a)

E ′B(FM, γ) = −FB(FM, γ) (3.37b)

FD(s) = χ(s)(FE1(s) + FEbrk(s)) + FE2(s) + Fbrk(s) + FM(s) (3.37c)

PB(FM, γ) = max
{
FM(s)
η

, ηFM(s)
}
v(s) + PMd(γ, FM) + PBd(PB) (3.37d)

χ(s)FE1(s) + FE2(s) ≤ ηPEmax

v(s) (3.37e)

FE1(s) ∈
[
0,min

{
b0, b1 + b2r

2(γ)v2(s)
}]
r(γ)η (3.37f)

FEbrk(s) ∈
[(
c1 + c2v(s)2r(γ)2

)
, 0
] r(γ)

η
(3.37g)

Fbrk(s) ≤ 0, FE2(s) ≥ 0 (3.37h)

FMmax(s) = min
{
d1, d2 + d3

v(s)r(γ)

}
r(γ)η (3.37i)

FMmin(s) = max
{
e1, e2 + e3

v(s)r(γ)

}
r(γ)
η

(3.37j)

EB(s0) = EB0, EB(sf) ≥ EBf (3.37k)

EB(s) ∈ [SOCmin, SOCmax]EBmax (3.37l)

χ+(s) = χ(s) + uχ(s), χ(s) ∈ X, uχ(s) ∈ Uχ (3.37m)

30



3. Methods

γ+(s) = γ(s) + uγ(s), γ(s) ∈ Γ, uγ(s) ∈ Uγ (3.37n)

However, the demanded force FD in (3.37c) has not been optimally divided between
the forces, which will be done in power split. Note that the penalty term Qtot has
been introduced, which is described as

Qtot = Wγ(γ) +Wχ(χ) + Fbrk(s)2Qbrk + FEbrk(s)2Qebrk + FE2(s)QFe2 (3.38)

where Qbrk, Qebrk and QFe2 are the penalties for applying Fbrk, FEbrk and FE2,
respectively. As FE2 should be avoided, QFe2 is put relatively high compared to the
other penalties. Since it is desirable to apply less Fbrk than FEbrk for braking, Qbrk
is put significantly higher than Qebrk.

The problem can be solved by first formulating a Hamiltonian which is expressed
as

H(FE, FB, γ, χ) = χµ̃(γ, FE) +Qtot − λB(s)FB(γ, χ, FM) (3.39)

A necessary condition for optimality is described by(
∂H
∂EB

)∗
− d

ds

(
∂H
∂E ′B

)∗
= 0 =⇒ λ′B(s) = 0 (3.40)

This means that λB should be constant over traveled distance for each predicted
horizon, provided that EB does not hit its limits, though it is likely to happen in
real scenario. However, for this project it is assumed that the battery is large enough
to avoid hitting the limits. Since λB should penalize the usage of EM as indicated
in Equation (3.39), it should also be negative.

3.8.1 Power split

When power split is performed, the gear γ and ICE-state χ have already been given
(later described in Section 3.8.2). For simplicity, instance s has also been omitted
in this section. A set of feasible FM-points (including FMmin and FMmax), which is
denoted by FMfeas, is first created

FMfeas ∈ {F1, F2, ..., FG} (3.41)

where G is the number of feasible FM-points. If FD also lies within the limits of FM,
then it also included in FMfeas.

31



3. Methods

The battery force FB, as function of FMfeas, needs to be expressed by using following
Equations

PM(FMfeas) = ωMrFMfeas (3.42)

PMd(FMfeas) = h1ωM + h2ω
3
M + h3ωMr

∣∣∣∣∣max
{
FMfeas

η
, ηFMfeas

}∣∣∣∣∣ (3.43)

PBd(PB) = R

V 2
oc
P 2

B (3.44)

PB = PM + PMd(FMfeas) + PBd(PB) = PM + PMd(FMfeas) + R

V 2
oc
P 2

B (3.45)

By solving the quadratic Equation (3.45) for PB, it can be expressed as

PB(FMfeas) = V 2
oc

2R −

√√√√( V 2
oc

2R2

)2

− V 2
oc
R

(PMd(FMfeas) + PM(FMfeas)) (3.46)

which is then used to express FB as

FB(FMfeas) = PB(FMfeas)
v

(3.47)

The rest of the control signals, as function of FMfeas, are calculated as

FE2(FMfeas) = max{0, FD − FMfeas − FEmax} (3.48a)

FE1(FMfeas) = max{0, FD − FMfeas − FE2(FMfeas)} (3.48b)

Fbrk(FMfeas) = min{0, FD − FMfeas − Febrkmin} (3.48c)

FEbrk(FMfeas) = min{0, FD − FMfeas − Fbrk(FMfeas)} (3.48d)

The limits for the force delivered by ICE in (3.48) are described by

FEmax = min
{
ηPEmax

v
, b0r(γ)η, (b1 + b2r

2(γ)v2)r(γ)η
}

(3.49a)

Febrkmin = (c1 + c2v
2r(γ)2)r(γ)

η
(3.49b)

The point from FMfeas which gives the least value of Hamiltonian in Equation (3.39)
becomes the optimal FM, which can then be used to obtain the rest of the optimal
control trajectories. However, the gear and ICE-state trajectories have not been
determined, which is done by dynamic programming [25].

32



3. Methods

3.8.2 Dynamic Programming

The states of DP (Dynamic Programming) are the gears and ICE-state, which can
be expressed as ζ(s) = [γ, χ]. It first performs backward optimization where the
initial instance is s = sf − 1 and then moves backward to reach next instance. For
every instance that has been reached and for every state, the optimization calculates
the minimum but feasible cost

J(ζ(s), s) = min
ζ(s+1)∈ζfeas

{C(ζ(s), ζ(s+ 1), s) + J(ζ(s+ 1), s+ 1)} (3.50)

where ζfeas = [Γfeas, Xfeas] are feasible updates of states at s + 1 and C(ζ(s)) is the
cost for being at the state at instance s.
The feasible state updates that can be reached at instance s+1 are expressed as

Γfeas = Γ ∩ (γ(s) + Uγ), Xfeas = X ∩ (χ(s) + Uχ) (3.51)

In the Hamiltonian cost (3.39), the penalties Wγ and Wχ have the weights wγ and
wχ, respectively. They are added based on the decision variables yγ and yχ, which
are described by

yγ(γ(s), γ(s+ 1)) =

1, if γ(s+ 1) < γ(s)
0, otherwise

(3.52a)

yχ(χ(s), χ(s+ 1)) =

1, if χ(s+ 1) 6= χ(s)
0, otherwise

(3.52b)

In other words, wγ is added when the selected gear at one instance is higher than
the selected gear at next instance due to downshift. The weight wχ is added when
the ICE-state is changed from one instance to the next. Both weights are tuned
accordingly to avoid frequent shifts.

Once the backward optimization has reached s = s0, the forward optimization be-
gins. It then chooses the optimal path with minimum cost among the costs of all
feasible paths. The optimal state at next instance can be expressed as

ζ∗(s+ 1) = arg min
ζ(s+1)∈ζfeas

{C(ζ∗(s), ζ(s+ 1), s) + J(ζ(s+ 1))} (3.53)

where ζ∗(s) is the optimal state at instance s.

3.8.3 Battery costate optimization

The battery costate trajectory λB, received from the energy management, is not
optimal as there is model miss-match between the two layers. This might lead

33



3. Methods

to that the final battery energy EB(sf) deviates significantly from its target EBf.
Therefore, λB needs to be adjusted iteratively [11][26] such that the battery energy
error ∆EBf satisfies

∆EBf = EB(sf)− EBf ≈ 0 (3.54)

Thus, for each iteration the dynamic programming needs to be run again to adjust
λB. The adjustment is done by increasing/decreasing with a stepsize δ. For example
if ∆EBf < 0, it means that too much EM-force has been applied and λB has to
decrease (λB := λB − δ) to penalize more and vice versa. If there has been a sign
change of calculated ∆EBf between two iterations, then EB(sf) has passed EBf, and
δ can be decreased with a factor to make better adjustments for next iterations. The
battery energy EB(s) can be obtained by integrating (3.37b) in space domain.

The procedure for updating λB is illustrated by the flow chart in Figure 3.6. It can
be described by following pseudocode where c is the iteration for updating λB:

1. Calculate ∆Ec
B(sf) after running dynamic programming.

2. If ∆Ec
B(sf) ≤ bound, then finish. Else move to step 3.

3. λcB = λc−1
B + sign(∆Ec

Bf)δ.

4. If sign(∆Ec
Bf) = −sign(∆Ec−1

Bf ) move to step 5. Else move to step 6.

5. δ := δ
2

6. c := c+ 1 and return to step 1.

Figure 3.6: Flow chart of the battery co-state update. The number of update is
denoted by c.

34



3. Methods

Both δ and c are reset to their initial values before the next MPC-update.

3.9 Summary of MPC-algorithm

A flowchart of the complete MPC-algorithm is shown in Figure 3.7, which can be
summarized by following steps:

1. Starting from the beginning of the road where current instance s0 = 0, the
position of leading vehicle is located and a constant cruising speed v̄ is set for
the host vehicle.

2. At s0, the host vehicle collects measurement data from the leading vehicle,
including its travel time and speed. The data is then sent to the leading
vehicle observer which estimates the parameters l0,l1 and l2.

3. Based on the estimated parameters and an assumed cruising speed v̄L, the
leading vehicle reference speed predictor obtains the reference speed trajectory
vLr. This trajectory is used to estimate the traveling time trajectory of leading
vehicle tL, which is then sent to both energy management and the host vehicle
speed predictor. The host vehicle speed predictor uses information of tL and
road topography to obtain host vehicle reference speed trajectory vr and send
it to the energy management.

4. In the energy management, the optimization problem is solved which yields the
optimal speed trajectory v and battery costate trajectory λB. Both trajectories
are sent to the power management. In the first iteration, the highest gear is
selected and ICE-state is on for all predicted instances.

5. The problem is solved in power management to find the optimal trajectories
for control signals, gear and ICE-state. It is solved repeatedly, until λB has
been updated such that EB(sf) lies within its bounds. The gear and ICE-state
trajectories are then sent to energy management.

6. If the solution has not converged or a maximum number of iteration has not
been reached, return to step 4. During each iteration, the reference speed
trajectory vr is updated as

vr := vr + (vr + (v − vr))β (3.55)

where β ∈ (0, 1] is a convergence step.

7. Apply the first element of the optimal control trajectories U(s0:sf) and discard
the rest. If the final instance of the road, sN, has been reached, finish the
procedure. Otherwise, move to the next instance and return to step 2.

35



3. Methods

Figure 3.7: Flow chart of the implemented MPC-algorithm

36



4
Results

In this chapter, the results obtained in this project are presented. For the driving
scenarios, two different road topographies are used:

1. An artificial driving cycle with a length of 7km as seen in Figure 4.1.

2. The second driving cycle is a road between Alingsås and Gothenburg as seen
in Figure 4.2. This is primarily used for investigating different case scenarios
which involve leading vehicle.

The investigations are done with host vehicle, both as CV and HEV. In Section 4.1,
the host vehicle driving on the road displayed in Figure 4.1 is shown to see how it
behaves without leading vehicle present. For the rest of the results, the driving cycle
in Figure 4.2 is used which involves leading vehicle. With leading vehicle present,
The length of predicted horizon is also examined. For all results, the sample distance
is set as 100m for prediction.

0 1 2 3 4 5 6 7

Traveled length[km]

0

10

20

30

40

50

60

70

R
o
a
d
 a

lt
it
u
d
e
[m

]

Figure 4.1: Artificial driving cycle with a road length of 7km. The horizontal axis
represents the traveled distance and the vertical axis represents the altitude.

37



4. Results

0 5 10 15 20 25 30 35 40

Traveled length[km]

0

10

20

30

40

50

60

70

80

90

100

R
o

a
d

 a
lt
it
u

d
e

[m
]

Figure 4.2: Road between Alingsås and Gothenburg. The length of the driving
cycle is 40.1km.

4.1 Validation of control algorithm without LV

In this section, the control algorithm is validated both for CV and HEV without a
leading vehicle present. Since there is no LV (Leading Vehicle) present, the predic-
tion horizon is set as the entire road and MPC needs to be run for one update only.
The cruising speed is set as v̄ = 80km/h. The speed tolerance is set as ± 10km/h,
meaning that the speed can deviate at most 10km/h from the reference speed.

4.1.1 CV without LV ahead

In Figure 4.3, the optimal speed and gear trajectories are shown with the speed
limits. There are some instances where the speed hits its limits, but it still remains
in the feasible region during the entire travel. The lowest selected gear is nine and
its trajectory does not downshift frequently.

38



4. Results

0

10

20

30

40

50

60

70

R
o

a
d

 a
lt
it
u

d
e

[m
]

0 1 2 3 4 5 6 7

Traveled length[km]

50

60

70

80

90

100

110

120

G
e

a
r

1
0

, 
s
p

e
e

d
[k

m
/h

]

Gear

Speed limits

Speed

Figure 4.3: The state trajectories of CV and the speed limits. The ICE-state is
not included since the engine is always on for CV.

The corresponding control trajectories to Figure 4.3 are depicted in Figure 4.4. In
the beginning where there is a very steep downhill, large frictional force by the
engine is applied such that it hits its limit. At one instance, the gear even needs to
be downshifted to apply even more frictional engine force. When traveling uphill,
the host vehicle starts applying engine force. Note that the engine force is never
applied at the same time as either braking or frictional engine force is. The abstract
force remains zero for the entire travel, so the gear trajectory has been properly
selected.

0

10

20

30

40

50

60

70

R
o

a
d

 a
lt
it
u

d
e

[m
]

0 1 2 3 4 5 6 7

Traveled length[km]

-15

-10

-5

0

5

10

15

20

F
o

rc
e

s
 a

t 
w

h
e

e
l 
s
id

e
[k

N
]

Engine force limit

Engine force

Abstract engine force

Braking force

Engine friction force limit

Engine friction force

Figure 4.4: The control trajectories of CV and ICE limits. EM force and its limits
are not displayed since they are not available for CV.

39



4. Results

4.1.2 HEV without LV ahead

In this case, EM force and SOC (the battery charge in percentage) are available.
The initial battery energy is assumed to be EB0 = 0.6EBmax and the targeted final
battery energy is chosen as EBf ≈ 0.4EBmax. Figure 4.5 displays the state trajecto-
ries of HEV, including its ICE-state and SOC, and Figure 4.6 displays the control
trajectories.

Compared to CV, HEV maintains higher gear trajectory as it is able to utilize force
from EM. Similar to the speed trajectory of CV, there are some instances where the
speed hits its limits but also remains within its feasible region. SOC increases when
EM works as generator (negative EM force applied) and decreases when EM works
as motor (positive EM force applied). However, SOC never hits its limits for the
entire travel.

0

10

20

30

40

50

60

70

R
o

a
d

 a
lt
it
u

d
e

[m
]

0 1 2 3 4 5 6 7

Traveled length[km]

0

20

40

60

80

100

120

IC
E

 s
ta

te
, 

G
e

a
r

1
0

, 
s
p

e
e

d
[k

m
/h

]

Gear

Speed limits

Speed

SOC limits

SOC (%)

ON/OFF 10

Figure 4.5: The state trajectories of HEV, including ICE-state and SOC, as func-
tion of traveled distance. The limits for SOC and speed are also displayed.

In the beginning, ICE is off and only negative EM force is applied. However, since
EM force reaches its limit later and more braking is required, an amount of frictional
force by the engine is applied as well and ICE has to be turned on. Positive EM force
is applied when HEV travels uphill, so that less engine force is needed for propulsion.
Note that in the interval 1-2.7km, where neither of the forces from engine is applied,
ICE is turned off again. EM force hits its upper limit at numerous instances.

40



4. Results

0

10

20

30

40

50

60

70

R
o

a
d

 a
lt
it
u

d
e

[m
]

0 1 2 3 4 5 6 7

Traveled length[km]

-8

-6

-4

-2

0

2

4

6

8

10

12

F
o

rc
e

s
 a

t 
w

h
e

e
l 
s
id

e
[k

N
]

Engine force limit

Engine force

Abstract engine force

Braking force

Engine friction force limit

Engine friction force

Em force limits

EM force

Figure 4.6: The control trajectories of HEV, including EM force, as function of
traveled distance. The limits for ICE and EM are also displayed.

4.2 Validation of control algorithm with LV

In this section, the control algorithm is evaluated when there is a leading vehicle
driving in front of host vehicle. Therefore, the leading vehicle observer has to be
used to estimate its power capability. Real measurement data of a leading vehicle
driving on the road topography in Figure 4.2 is used.

The leading vehicle is assumed to have been detected at 200m from the start of the
road. Therefore, a new MPC-update is made for each instance that host vehicle
reaches. Since it is unknown of what the desired speed of leading vehicle v̄L is,
it is set as the average value of the collected measured speed between updates or
as minimum 60km/h. The length of prediction horizon is set as Sp=4km and the
desired speed of host vehicle is set as v̄ =90km/h. For the safety constraint, the
time headway is set as ∆t =2s.

4.2.1 LV observer

Figure 4.7 shows the performance of observer dependent on the traveled distance of
leading vehicle along with its actual acceleration limit. The further leading vehicle
travels, the more measurements are collected. A sample distance of 5m is used to
collect the measurement data. The number of speed clusters is chosen as 10.

41



4. Results

30 40 50 60 70 80

Vehicle speed[km/h]

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

A
c
c
e
le

ra
ti
o
n
s
[m

/s
2
]

Actual a
max

0.2km

1km

5km

10km

20km

39.785km

Figure 4.7: The various estimated acceleration limits as function of vehicle speed.
The estimation of limits depend on the traveled distance of leading vehicle.

All estimated limits are non-concave due to the boundaries put for the parameters.
The limit that is obtained after leading vehicle has driven only for 200m is the
one that deviates most from the actual limit, as there is not enough measured
points collected to make a proper estimation. However, after the leading vehicle has
driven further, more measurement data is collected and the observer makes better
estimation of the limit. The various estimated accelerations limits obtained after
leading vehicle has driven 1km and further are closer to the actual limit compared
to the one when the leading vehicle has only driven for 200m.

4.2.2 CV with LV ahead

The state trajectories, which include gear and speed, are seen in Figure 4.8. Since
the desired speed v̄ is now set higher than in Section 4.1 and the speed needs to be
adjusted to not get too close to leading vehicle, the speed limits vary a lot more.
The speed hits the limits at some instances, but remains within its feasible region
during the entire travel.

42



4. Results

0

10

20

30

40

50

60

70

80

90

100

R
o

a
d

 a
lt
it
u

d
e

[m
]

0 5 10 15 20 25 30 35 40

Traveled length[km]

40

50

60

70

80

90

100

110

120

G
e

a
r

1
0

, 
s
p

e
e

d
[k

m
/h

]

Gear

Speed limits

Speed

Figure 4.8: The state trajectories of CV as function of traveled distance and the
speed limits.

The control trajectories of host vehicle is seen in Figure 4.9. Note that at instance
7.9km where there is a very steep downhill, the gear has to be downshifted to a
much lower level to be able to apply much larger frictional force by the engine. For
uphills, the engine force is applied. Neither abstract force nor mechanical braking
force (braking force by the service brake) is applied for the entire travel.

0

10

20

30

40

50

60

70

80

90

100

R
o
a
d
 a

lt
it
u
d
e
[m

]

0 5 10 15 20 25 30 35 40

Traveled length[km]

-30

-20

-10

0

10

20

30

F
o
rc

e
s
 a

t 
w

h
e
e
l 
s
id

e
[k

N
]

Engine force limit

Engine force

Abstract engine force

Braking force

Engine friction force limit

Engine friction force

Figure 4.9: The control trajectories of CV as function of traveled distance and the
ICE limits.

43



4. Results

Figure 4.10 shows the gap between the traveling times of host and leading vehicle.
There are some instances where the gap goes a little bit below the time headway.
However, the most important thing is that it never goes to 0, meaning that host ve-
hicle never collides with leading vehicle. Note that gap is biggest at around 32.5km.
This could be that the calculated desired speed of leading vehicle is significantly
lower than the actual desired speed, which makes the gap bigger as host vehicle
drives slower.

0

10

20

30

40

50

60

70

80

90

100

R
o

a
d

 a
lt
it
u

d
e

[m
]

5 10 15 20 25 30 35 40

Traveled length[km]

0

2

4

6

8

10

12

14

16

18

20

T
im

e
[s

]

Time gap

t

Figure 4.10: The time gap between the traveling times of leading vehicle and host
vehicle (CV) as function of traveled distance.

4.2.3 HEV with LV ahead

In the beginning of the road, the battery energy is assumed to be EB0 = 0.6EBmax.
For simplicity, λB should be updated such that the targeted battery energy becomes
EBf ≈ 0.6EBmax by the end of horizon.

Figure 4.11 shows the state trajectories of host vehicle as HEV. Compared to Figure
4.8, the gear trajectory is higher. The lowest selected gear is 10, but the trajectory
remains on gear 12 during most of the travel. SOC varies during travel, but never
hits its limits. Except for the instances around 28-29km and in the beginning of the
road, the ICE-state does not shift frequently between the updates.

44



4. Results

0

10

20

30

40

50

60

70

80

90

100

R
o

a
d

 a
lt
it
u

d
e

[m
]

0 5 10 15 20 25 30 35 40

Traveled length[km]

0

20

40

60

80

100

120

IC
E

 s
ta

te
, 

G
e

a
r

1
0

, 
s
p

e
e

d
[k

m
/h

]

Gear

Speed limits

Speed

SOC limits

SOC (%)

ON/OFF 10

Figure 4.11: The state trajectories of HEV as function of traveled distance. The
limits for SOC and speed are also displayed.

Figure 4.12 illustrates the control trajectories and their limits. Positive EM force
is applied when going uphill and sometimes requires ICE to be turned on to apply
engine force as well. There are some instances where negative EM force and engine
force are applied at the same time, which is sometimes needed to charge the battery.
When traveling downhill, negative EM force is applied to brake and generate energy
to the battery. However, since there are some instances where the downhill is very
steep, ICE still needs to be turned on to apply frictional engine force as EM force
has already reached its limit. Since the abstract force is never applied during the
entire travel, the gear trajectory has been properly selected.

0

10

20

30

40

50

60

70

80

90

100

R
o

a
d

 a
lt
it
u

d
e

[m
]

0 5 10 15 20 25 30 35 40

Traveled length[km]

-15

-10

-5

0

5

10

15

F
o

rc
e

s
 a

t 
w

h
e

e
l 
s
id

e
[k

N
]

Engine force limit

Engine force

Abstract engine force

Braking force

Engine friction force limit

Engine friction force

Em force limits

EM force

Figure 4.12: The control trajectories of HEV as function of traveled distance. The
limits for ICE and EM are also displayed.

The time gap is illustrated in Figure 4.13. It is shown in the Figure that the host

45



4. Results

vehicle maintains a safe distance to the leading vehicle throughout the driving cycle.
There are a few instances where the gap goes a little bit below ∆t, but it never gets
close to 0. This means that host vehicle never gets too close or collides with leading
vehicle in front.

0

10

20

30

40

50

60

70

80

90

100

R
o

a
d

 a
lt
it
u

d
e

[m
]

5 10 15 20 25 30 35 40

Traveled length[km]

0

5

10

15
T

im
e

[s
]

Time gap

t

Figure 4.13: The time gap between the traveling times of leading vehicle and host
vehicle (HEV) as function of traveled distance.

By comparing the results of CV and HEV in Figures 4.8 and 4.11, it is shown that
HEV does not need to downshift the gear as frequently as CV. This is because EM
supports ICE for delivering demanded force. In Figures 4.9 and 4.12, it can be seen
that the HEV applies less frictional force by the engine as it is able to use EM for
braking. By using EM for braking, the HEV also recovers energy and stores it in
the battery, which is later used for propulsion.

4.3 Length of prediction horizon

In this section, the length of prediction horizon is examined to see how it affects the
performance of the control algorithm. Same driving scenario with similar settings
as described in Section 4.2 are used here.

Table 4.1 shows the fuel consumption and final traveling time of host vehicle as
CV for other selected lengths of prediction horizon. It also includes tsum, which is
the sum of the time gap going below ∆t. In other words, tsum shows how much
the safety constraint has been violated during the entire travel. For the case when
the prediction horizon is set as the entire road length, MPC is run for one update
only.

46



4. Results

Table 4.1: Fuel consumption, final traveling time and tsum of CV for different
prediction horizon.

Sp[km] Fuel[kg] tf[min] tsum[s]
Entire road length 6.9163 39.953 0

1 7.7115 30.0816 10.09
2 5.9472 30.0758 5.43
3 5.9576 30.0814 4.05
4 5.402 30.0727 4.83

For the shorter prediction horizons (1-4km), it can be seen that the highest fuel
consumption is for the case with Sp=1km and lowest for the case with Sp=4km.
Normally, what is expected is that the fuel consumption will monotonically decrease
the longer prediction horizon is as more instances of the road topography ahead are
taken into consideration. However, the fuel consumption for the case with Sp=3km
is slightly higher compared to the one for the case with Sp=2km. It is shown
that the host vehicle travels faster and also uses more engine braking in the case
with Sp=3km than Sp=2km. This is likely because of uncertainty of the leading
vehicle speed prediction at some instances for Sp=3km. For some MPC-updates, the
host vehicle predicts that the leading vehicle will travel faster, but then it predicts
that the leading vehicle travel will travel significantly slower in the next update.
Therefore, the host vehicle drives faster first but then it has to apply more engine
brake as it predicts the leading vehicle will drive significantly slower in the next
update. Thus, fuel consumption, which is the function of speed and engine force as
shown in Equation (2.9), is higher for the case with Sp=3km.

A similar table for HEV is shown in Table 4.2. The initial battery energy EB0 and
targeted final battery EBf have been set the same as in Section 4.2.3, regardless of
length of prediction horizon.

Table 4.2: Fuel consumption, final traveling time and tsum of HEV for different
lengths of prediction horizon.

Sp[km] Fuel[kg] tf[min] tsum[s]
Entire road length 1.3408 39.953 0

1 3.5025 30.0824 8.48
2 3.26 30.0728 3.80
3 2.8474 30.0807 0.44
4 2.3425 30.0907 1.1825

With HEV, the fuel consumption decreases the longer horizon that is selected as
more instances of the road topography are taken into consideration.

Note that for both CV and HEV, tsum is 0 but the final traveling time is much
longer when the prediction horizon is set as the entire length and run for one update
only. This can be explained by Figure 4.14 which shows a comparison between the

47



4. Results

predicted and actual speed of leading vehicle and its constant desired speed which
has been assumed to be 60km/h. Since the leading vehicle has been detected at
200m from the beginning of the road, the observer has estimated its acceleration
limit as the one shown in Figure 4.7 after it has driven 0.2km. With the acceleration
limit, the speed leading vehicle been predicted to maintain its assumed desired speed
for the entire road.

However, except for the instance around 8km, the predicted speed is considerably
lower than the actual one for the entire travel. This means that host vehicle believes
that the leading vehicle drives significantly slower than it actually does, which leads
to the host vehicle also drives slower. Therefore, the safety constraint is never
violated, but the time gap between the vehicles increases over traveled distance and
the final travel time of host vehicle is longer compared to the cases with shorter
prediction horizons.

5 10 15 20 25 30 35 40

Traveled length[km]

50

55

60

65

70

75

80

85

90

95

S
p

e
e

d
[k

m
/h

]

Actual speed

Predicted speed

Assumed desired speed

Figure 4.14: The actual and predicted speed of leading vehicle and its assumed
desired speed when the prediction is done once for the entire road.

Figures 4.15 and 4.16 show the time gaps for different lengths of prediction horizon
as function of traveled distance for CV and HEV, respectively. As the results of
tsum in Tables 4.1 and 4.2 indicate, the safety constraint has been violated for the
shorter prediction horizons. But most importantly, neither of them gets close to or
below 0. For both CV and HEV, the safety constraint is never violated for the case
where prediction horizon is set as the entire road length, but the gap increases over
traveled distance.

48



4. Results

0

10

20

30

40

50

60

70

80

90

100

R
o

a
d

 a
lt
it
u

d
e

[m
]

5 10 15 20 25 30 35 40

Traveled length[km]

0

5

10

15

20

25

T
im

e
[s

]

Sp=1km

Sp=2km

Sp=3km

Sp=4km

Entire road

t

Figure 4.15: Time gaps for different lengths of prediction horizon as function of
traveled distance for CV. Note that the rest of the gap represented by the black line
is not displayed as it increases significantly over traveled distance.

0

10

20

30

40

50

60

70

80

90

100

R
o

a
d

 a
lt
it
u

d
e

[m
]

5 10 15 20 25 30 35 40

Traveled length[km]

0

5

10

15

20

25

T
im

e
[s

]

Sp=1km

Sp=2km

Sp=3km

Sp=4km

Entire road

t

Figure 4.16: Time gaps for different lengths of prediction horizon as function of
traveled distance for HEV.

4.4 No observer available

In this section, similar case scenario as described in Section 4.2 is examined when
the observer is not available. Only HEV as host vehicle is considered and the same

49



4. Results

settings described in Section 4.2.3 are used. This case is important to study the
benefit of the observer when comparing with the results in Section 4.2.3.

For each MPC-update, only the current speed of leading vehicle is measured and
the host vehicle assumes it to be constant over the predicted horizon. If the current
speed of leading vehicle is less than 60km/h, the host vehicle assumes that leading
vehicle will maintain a constant speed of 60km/h.

The control trajectories are seen in Figure 4.17. Compared to Figure 4.12, a sig-
nificantly larger frictional force by engine is applied along with force by service
brake at around 8km in this case. This is because the host vehicle can only assume
that leading vehicle will maintain its current speed over predicted horizon. In the
next MPC-update however, the current speed of leading vehicle is measured to be
lower and host vehicle needs to slow down significantly by applying more braking
force.

0

10

20

30

40

50

60

70

80

90

100

R
o
a
d
 a

lt
it
u
d
e
[m

]

0 5 10 15 20 25 30 35 40

Traveled length[km]

-20

-15

-10

-5

0

5

10

15

20

F
o
rc

e
s
 a

t 
w

h
e
e
l 
s
id

e
[k

N
]

Engine force limit

Engine force

Abstract engine force

Braking force

Engine friction force limit

Engine friction force

Em force limits

EM force

Figure 4.17: The control trajectories as function of traveled distance when the
observer is not available.

The time gap between host and leading vehicle is shown in Figure 4.18. There
are some instances where the gap goes below ∆t, but it never reaches 0. However,
compared to Figure 4.13, the safety constraint is more violated in this case.

50



4. Results

0

10

20

30

40

50

60

70

80

90

100

R
o

a
d

 a
lt
it
u

d
e

[m
]

5 10 15 20 25 30 35 40

Traveled length[km]

0

5

10

15

T
im

e
[s

]

Time gap

t

Figure 4.18: The time gap as function of traveled distance when the observer is
not available.

Figure 4.19 shows the predicted speed trajectories of leading vehicle along with its
actual speed trajectory. The assumed desired speed for each sample is also shown.
As the current speed of leading vehicle is assumed to be constant over predicted
horizon for each update, the predicted speed trajectories deviate significantly from
the actual trajectory.

5 10 15 20 25 30 35 40

Traveled length[km]

45

50

55

60

65

70

75

80

85

90

95

S
p

e
e

d
[k

m
/h

]

Actual speed

Predicted speed

Assumed desired speed

Figure 4.19: The predicted speed trajectory and the assumed desired speed of the
leading vehicle for each sample along with the actual speed trajectory when observer
is not available.

51



4. Results

Note that for those updates where the current speed is lower than 60km/h, the host
vehicle assumes that leading vehicle maintains 60km/h over predicted horizon.

Figure 4.20 shows the predicted speed trajectories of leading vehicle along with its
actual speed trajectory for the case in Section 4.2.3 where observer is used.

5 10 15 20 25 30 35 40

Traveled length[km]

45

50

55

60

65

70

75

80

85

90

95

S
p

e
e

d
[k

m
/h

]

Actual speed

Predicted speed

Assumed desired speed

Figure 4.20: The predicted speed trajectory and the assumed desired speed of the
leading vehicle for each sample along with the actual speed trajectory when observer
is used.

Compared to Figure 4.19, the predicted speed trajectories are closer to the ac-
tual speed trajectory which is shown at some instances such as around 16km and
27km.

However, most of the predicted trajectories still do not align with the actual trajec-
tory. The main reason is likely that the desired speed of leading vehicle has been
wrongly assumed, and not because of the acceleration limit has been poorly esti-
mated. The observer seems to give a good estimation of the limit just after leading
vehicle has driven 1km which is seen in Section 4.2.1. Since the road topography
mainly includes downhills, some of the predicted speed trajectories show that the
speed is constant over predicted horizon, similar to the case where observer is not
available.

52



4. Results

4.5 Benefit of HEV

In this section, the benefit of HEV is discussed.

Figure 4.21: Fuel consumption of CV and HEV for different lengths of prediction
horizon.

Figure 4.21 shows the fuel consumed by CV and HEV for different prediction horizon
lengths. It is shown that the HEV consumes less fuel compared to CV regardless of
length of the prediction horizon. As explained earlier, the HEV is able to recover
energy by using EM for braking. The energy is stored in the battery and is later
used for propulsion of HEV. In addition to this, it also allows ICE to be turned off
during certain periods where the EM is able to provide all the necessary power, thus
decreasing the fuel consumption further.

4.6 Benefit of having prediction horizon

In this section, the benefit of having different prediction horizon length is discussed.
Tables 4.1 and 4.2 show the fuel consumption and final travel time of CV and HEV
for different horizon lengths, respectively. From the tables, it can be seen that
choosing an optimal prediction horizon length is necessary. When analysing the
benefit of prediction horizon length, it is more reasonable to consider the final travel
time along with the fuel consumed for each horizon length.

In Figures 4.22 and 4.23, the final travel time and fuel consumed by HEV for different
prediction horizons and for the entire road (40.1km) are shown. For the shorter
prediction horizons (1-4km), the fuel consumed is higher and it decreases as the
prediction horizon length increases. The final travel time does not differ significantly
for prediction horizons 1-4km. For the case where the prediction horizon length is
set as the entire road, the MPC is run for one update only. It is observed that this
case has the lowest fuel consumption, but also the highest final travel time. The
reason is that the speed of leading vehicle is predicted lower than its actual speed.
Therefore, the host vehicle drives significantly slower, resulting in longer travel time.

53



4. Results

Figure 4.22: The final travel time of
HEV for different horizons and for the
entire road (40.1km).

Figure 4.23: The fuel consumed by
HEV for different horizons and for the
entire road (40.1km).

Figure 4.24: The final travel time of
CV for different horizons and for the
entire road (40.1km).

Figure 4.25: The fuel consumed by
CV for different horizons and for the
entire road (40.1km).

The fuel consumption is lowest since ICE remains off for longer periods compared
to the other horizons as EM can deliver the demanded force needed for the host
vehicle to drive with lower speed.

In Figures 4.24 and 4.25 the final travel time and fuel consumed by CV for different
prediction horizons and for the entire road (40.1km) are shown. It is observed that
fuel consumption and final travel time behaviour for prediction horizon lengths 1-
4km of CV are similar to HEV. But for the case where the prediction horizon is
set as entire road length, the travel time is same but fuel consumption behaviour is
quite different from the HEV. For CV, it has to maintain lower gear trajectory as
it requires more frictional force by the engine to maintain lower speed, leading to
higher fuel consumption.

54



5
Discussion

This Chapter includes discussion of the results, but also different areas of the work
are discussed and how they can be improved for future work.

5.1 Leading vehicle observer and speed predic-
tion

As seen in Figure 4.7, the estimation of acceleration limit gets better for the limits
where leading vehicle has driven further as more data has been collected. However,
more collected measurement data does not necessarily mean that it gives better
estimation as it can also introduce more noisy measurement points which will affect
the estimation negatively if noise-counters miss them.

For leading vehicle speed predictor, it has to be assumed that the desired speed of
leading vehicle is known. As for the real measurement data, the desired speed of
leading vehicle was unknown. As it was also unknown what the maximum allowed
speed was for the road, the desired speed was simply assumed to be the average of
the collected measured speed during each MPC-update or minimum 60km/h. This
greatly influences the results as even if the observer makes a good estimation of
the acceleration limit, the prediction can still be bad if the desired speed is guessed
poorly. For example, if the actual desired speed is lower than the assumed one,
the risk is greater that the host vehicle collides with leading vehicle. If the desired
speed of leading vehicle is set as lower than the actual one, host vehicle might drive
slower than it should. Knowing the maximum allowed speed of the road would be
beneficial, as that could give a hint of what speed leading vehicle wants to maintain.
The desired speed could instead be calculated as the average value of the collected
measured speed or the maximum allowed speed.

The benefit from using observer is explained in Section 4.4. It is indicated that
using an observer improves the leading vehicle speed prediction compared to not
using it. This leads to reduced energy consumption and less usage of service brakes.
In addition, the safety constraint is less violated when using the observer. However,
measurement data of road topography with more uphills is needed to further validate
the observer.

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5. Discussion

5.2 Measurement data and road topography

As mentioned earlier, the road topography mainly includes downhills, which is likely
the main reason for the huge fuel reduction for HEV, regardless of horizon length.
As there are mainly downhills included, the observer is also less useful for this kind of
topography. If topography mainly consisted of uphills however, it would have been
more unlikely for the leading vehicle to maintain its desired speed and an observer
would then be more useful.

The length of road used for the driving scenarios is also significantly shorter than
what a truck normally drives. Measurement data of trucks driving on longer road
would therefore be more beneficial to further validate the control algorithm.

For this thesis, it is assumed that the only traffic on the road is the leading vehicle.
However, we are not certain of whether there were other obstacles that might affect
the driving behaviour of the leading vehicle or not with this measurement data,
although it is likely to be the case.

5.3 Choice of prediction horizon

As discussed in Section 4.6, choosing optimal prediction horizon length is neces-
sary. The shorter prediction horizon and the entire road length as the prediction
horizon length are not the optimal choice which is shown in Section 4.6 in detail.
When choosing the optimal prediction horizon length, it is necessary to compare
the parameters such as fuel consumption, final travel time and the safety constraint
(tsum) as shown in Tables 4.1 and 4.2. Other parameters such as type of host ve-
hicle (HEV or CV) and the road topography also influence the choice of prediction
horizon length. Another thing to point out is that the mass was set as 40ton for
both CV and HEV. In reality however, an HEV might be heavier as it includes both
electric machine and battery, adding additional weight to the vehicle.

5.4 Ethic and sustainability

By successfully implementing this kind of control algorithm, better fuel efficiency
can be achieved. Increased fuel efficiency reduces fuel consumption which means less
emission of greenhouse gases to the environm