Adaptive tracking-type games for coupled large population ARMAX systems

Distributed adaptive tracking-type games is investigated for large population stochastic multi-agent systems. The dynamics of each agent is described by ARMAX model with unknown structure parameters and unknown coupled terms. The performance index has an unknown population state average (PSA) term. In order to deal with the uncertainties, the extended least-squares algorithm is used to estimate the unknown parameters, and the Nash certainty equivalence principle is used to estimate the unknown PSA term. Based on the certainty equivalence principle in adaptive control theory, a distributed adaptive tracking control is designed, under which the closed-loop system is shown to have the following properties: (1) the closed-loop system is almost surely uniformly stable with respect to the population number N; (2) the estimation of PSA is strongly consistent; (3) the adaptive control is almost surely asymptotically optimal in the sense of Nash equilibrium. A numerical example is given to demonstrate the results.