Optimal Consensus Control for Heterogeneous Nonlinear Multiagent Systems with Partially Unknown Dynamics

Abstract

This paper focuses on an optimal consensus problem for heterogeneous discrete-time nonlinear multi-agent systems (MASs) with partially unknown dynamics. For those systems, it is difficult to obtain the solution of the coupled Hamilton-Jacobi-Bellman (HJB) equations, which is necessary to address the optimal consensus problem. A new hierarchical and distributed optimal control strategy is developed to derive the near solution of the HJB equations. Its control structure consists of the model reference adaptive control (MRAC) layer and distributed control layer. In the MRAC layer, the adaptive feedforward and feedback controller is designed to make the states of followers converge to ones of their corresponding reference models. Then, the optimal consensus problem of heterogeneous MASs is formulated as that of homogeneous MASs. In the distributed control layer, an online distributed value iteration algorithm is proposed to approximate the optimal solution of the HJB equations for reference models. Thereby, the optimal consensus is also achieved for the heterogeneous MASs. The two convergence properties are analyzed to demonstrate the MRAC performance and the optimal consensus, respectively. Simulation results verify the effectiveness of the proposed strategy.