TY - JOUR
T1 - Robust mean field games for coupled Markov jump linear systems
AU - Moon, Jun
AU - Başar, Tamer
N1 - Funding Information:
The first author was supported in part by the Fulbright Commission. This research was supported in part by the U.S. Air Force Office of Scientific Research (AFOSR)MURI[grant number FA9550-10-1-0573]
PY - 2016/7/2
Y1 - 2016/7/2
N2 - 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.
AB - 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.
KW - LQG control
KW - Markov jump linear systems
KW - Mean field games
KW - stochastic zero-sum differential games
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U2 - 10.1080/00207179.2015.1129560
DO - 10.1080/00207179.2015.1129560
M3 - Article
AN - SCOPUS:84954147628
VL - 89
SP - 1367
EP - 1381
JO - International Journal of Control
JF - International Journal of Control
SN - 0020-7179
IS - 7
ER -