ADP‐based robust consensus for multi‐agent systems with unknown dynamics and random uncertain channels

Abstract

This article pursues the robust consensus for linear discrete‐time multi‐agent systems with unknown dynamics and random uncertain channels. Stochastic multiplicative uncertainties depending on relative states of agents inevitably appear in the signal transmission channels. To handle these uncertainties, the distributed robust controllers are designed. Before designing this robust controller, the optimal control problem of a single‐agent system is considered first. Based on the technology of adaptive dynamic programming, a model‐free off‐policy algorithm is proposed to solve the optimal controller for every agent with fully unknown system dynamics. According to the theory of mean square stability, it is revealed that the distributed robust controller can be obtained by using the optimal controller of the single‐agent system and other related parameters without relying on the dynamic information of the systems. Besides, the relationship between uncertainty and the robust controller is described by a sufficient condition. Finally, to demonstrate the effectiveness of the theoretical analysis, a numerical example is presented.