Distributed Adaptive Dynamic Programming for Optimal Cluster Synchronization of Multicluster Games Against Unknown Perturbation
针对多智能体系统在未知扰动下的最优簇同步问题，提出一种结合扰动观测器和自适应动态规划的控制方法，使系统达到广义纳什均衡。
This article studies the optimal cluster synchronization (OCS) problem for multiagent systems (MASs) with the unknown perturbation under a multicluster game (MCG) framework. To estimate the unknown perturbation, a novel perturbation observer nested with a parameter adaptive law is first designed. Subsequently, a coupling performance index function relevant to the synchronization error and the control policy with the quadratic form is constructed. By utilizing the distributed adaptive dynamic programming (ADP) technology with a single-critic architecture, the optimal control policy is designed by solving the Hamilton–Jacobi–Bellman (HJB) equation associated with the coupling performance index function. Meanwhile, an adaptive OCS control policy with a single-critic neural network (NN) updating law is further proposed, and it is proven that the designed adaptive OCS control policy constitutes the generalized Nash equilibrium (GNE) point of the MCG. Based on the Lyapunov extension theorem, all signals of the closed-loop MASs are ensured to be bounded. Finally, a simulation example is presented to validate the effectiveness of the proposed adaptive OCS control method.