Distributed consensus for nonlinear multi-agent systems with two-time-scales: A hybrid reinforcement learning consensus algorithm

Abstract

The optimal consensus problem for nonlinear two-time-scales multi-agent systems with completely unknown system dynamics is investigated in this paper. First, the original system is linearly represented based on the Takagi-Sugeno fuzzy model. Then, the optimal consensus problem for multi-agent systems is transformed into solving the game algebraic Riccati equation associated with agents and their neighbors. And individual agent dynamics studied in this paper are replaced with local error dynamics. Moreover, an offline hybrid iteration algorithm with rapid convergence speed and no initial stable control policy is presented for multi-agent systems. Meanwhile, to avoid the utilization of the knowledge of system matrices, an online hybrid reinforcement learning algorithm that only uses the state and control input data of each agent and its neighbors is given to generate the distributed optimal control policy. The convergence of proposed algorithms is also discussed. Finally, the applicability of the presented method is illustrated by an example.