Robust adaptive control of coupled stochastic multi-agent systems with unmodeled dynamics

Distributed robust adaptive control is investigated for a class of stochastic multi-agent systems with unknown time-varying structure parameters, unmodeled dynamics, external disturbances, and interactions among agents. The control goal is to make the states of all the agents converge to a desired function of the population state average (PSA). Due to the fact that only local information is available for each agent, the control is distributed. The key techniques adopted here to cope with the uncertainties are normalized projected least mean square algorithm, Nash certainty equivalence principle and certainty equivalence principle, which are used for estimating the unknown time-varying parameters and unknown PSA term, and designing adaptive control, respectively. Under some mild conditions, the stability of the closed-loop system, consistence of the PSA estimate, and robust Nash equilibrium property of the control laws are obtained. A numerical example is given to illustrate the results.