Data-Based Optimal Synchronization Control for Discrete-Time Nonlinear Heterogeneous Multiagent Systems

This article investigates the optimal synchronization problem for unknown discrete-time nonlinear heterogeneous multiagent systems (MASs). It is very intractable to derive the analytical solutions of coupled Bellman's equations, which are necessary to overcome this problem. We propose a data-based optimal synchronization control strategy based on a hierarchical and distributed optimal control framework composed of a model reference adaptive control (MRAC) layer and a distributed control layer. In the MRAC layer, the similar-offline MRAC algorithm is developed to make subsystems of MASs track their reference models, respectively. Then, the distributed optimal control problem of nonlinear heterogeneous MASs is transformed into that of homogeneous MASs composed of the reference models and the leader. In the distributed control layer, the distributed reference policy iteration algorithm is proposed to derive the solutions of coupled composite nonlinear Bellman's equations, which ensure that the homogeneous MASs reach synchronization with optimum. The suboptimal synchronization control is achieved via optimization further. Convergence analysis of both algorithms is rigorously provided. The simulation results verify the effectiveness of the proposed strategy.