Robust mean field games for coupled Markov jump linear systems

Jun Moon, Tamer Başar

Research output: Contribution to journalArticlepeer-review

Abstract

We consider robust stochastic large population games for coupled Markov jump linear systems (MJLSs). The N agents’ individual MJLSs are governed by different infinitesimal generators, and are affected not only by the control input but also by an individual disturbance (or adversarial) input. The mean field term, representing the average behaviour of N agents, is included in the individual worst-case cost function to capture coupling effects among agents. To circumvent the computational complexity and analyse the worst-case effect of the disturbance, we use robust mean field game theory to design low-complexity robust decentralised controllers and to characterise the associated worst-case disturbance. We show that with the individual robust decentralised controller and the corresponding worst-case disturbance, which constitute a saddle-point solution to a generic stochastic differential game for MJLSs, the actual mean field behaviour can be approximated by a deterministic function which is a fixed-point solution to the constructed mean field system. We further show that the closed-loop system is uniformly stable independent of N, and an approximate optimality can be obtained in the sense of ε-Nash equilibrium, where ε can be taken to be arbitrarily close to zero as N becomes sufficiently large. A numerical example is included to illustrate the results.

Original languageEnglish (US)
Pages (from-to)1367-1381
Number of pages15
JournalInternational Journal of Control
Volume89
Issue number7
DOIs
StatePublished - Jul 2 2016

Keywords

  • LQG control
  • Markov jump linear systems
  • Mean field games
  • stochastic zero-sum differential games

ASJC Scopus subject areas

  • Control and Systems Engineering
  • Computer Science Applications

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