Stochastic Differential Games and Decentralized Control
Publicerad
Författare
Typ
Examensarbete för masterexamen
Master's Thesis
Master's Thesis
Modellbyggare
Tidskriftstitel
ISSN
Volymtitel
Utgivare
Sammanfattning
Multi-agent stochastic control games naturally give rise to coupled forward backward
stochastic differential equations (FBSDE) for each agent. In such cases, dependencies
exist both between the forward and backward equations and across agents,
resulting in a highly non-trivial system to solve. In this thesis, a novel solution algorithm
for such systems is presented, that is more robust compared to the existing
Deep Fictitious Play method. The algorithm presented has been validated through
several numerical examples. An analytical solution for linear–quadratic–Gaussian
differential games is derived to validate the algorithm for problems where the Deep
Fictitious Play algorithm has been shown to fail. This demonstrates the improved
capabilities compared to the algorithms in the literature. In addition, a complex
numerical example is designed that models a heterogeneous stochastic control game,
which describes a swarm of drones following a predefined trajectory.
Beskrivning
Ämne/nyckelord
Stochastic differential equation, Forward backward differential equation, Game theory, Stochastic control, Fictitious play, Multi-agent games.