Stabilization of decentralized adaptive control for nonlinearly parametrized coupled stochastic multiagent systems

In this paper, the decentralized adaptive control is investigated for a class of discrete-time stochastic multiagent systems, where each agent is evolved according to a nonlinear discrete-time autoregressive model with the unknown parameter and unknown coupled terms, and the dynamics of any agent is coupled to other agents through its individual neighbors history information and is influenced by stochastic disturbances. Unlike some existing researches, this contribution considers both strong coupling uncertainties and nonlinear parametric uncertainties as well as random noise disturbances, which make the design and analysis of decentralized adaptive control quite difficult and challenging. For dealing with these uncertainties, the nonlinear least-squares algorithm is used as one reasonable approach to estimate the unknown parameters, which serves as the key foundation of the decentralized adaptive control. Based on the implicit function existence theorem, the decentralized adaptive control is designed, under which the stability of the closed-loop system is explicitly established with the following properties: (1) the parameter estimates of agents converge to the corresponding true values with convergence rate analyzed with the techniques of order estimation and inequality analysis initiated by Chen and Guo; (2) the global nonlinear growth rate supreme b^∗ in some sense is related to not only the number N of agents but also nonlinear growth rates of agents; and (3) the closed-loop system is stable almost surely in the presence of the uncertain strong couplings.