School of Mechanical and Electrical Engineering, Guangzhou University, Guangzhou, 510006, Guangdong, China; School of Mathematics, Southeast University, Nanjing, 211189, China; Department of Mathematical Sciences, Seoul National University, Seoul, 08826, Republic of Korea.
School of Mechanical and Electrical Engineering, Guangzhou University, Guangzhou, 510006, Guangdong, China.
Neural Netw. 2024 Nov;179:106566. doi: 10.1016/j.neunet.2024.106566. Epub 2024 Jul 25.
This paper studies an optimal synchronous control protocol design for nonlinear multi-agent systems under partially known dynamics and uncertain external disturbance. Under some mild assumptions, Hamilton-Jacobi-Isaacs equation is derived by the performance index function and system dynamics, which serves as an equivalent formulation. Distributed policy iteration adaptive dynamic programming is developed to obtain the numerical solution to the Hamilton-Jacobi-Isaacs equation. Three theoretical results are given about the proposed algorithm. First, the iterative variables is proved to converge to the solution to Hamilton-Jacobi-Isaacs equation. Second, the L-gain performance of the closed loop system is achieved. As a special case, the origin of the nominal system is asymptotically stable. Third, the obtained control protocol constitutes an Nash equilibrium solution. Neural network-based implementation is designed following the main results. Finally, two numerical examples are provided to verify the effectiveness of the proposed method.
本文研究了部分未知动态和不确定外部干扰下非线性多智能体系统的最优同步控制协议设计。在一些温和的假设下，通过性能指标函数和系统动力学推导出哈密顿-雅可比-伊萨亚斯方程，作为等效公式。开发分布式策略迭代自适应动态规划来获得哈密顿-雅可比-伊萨亚斯方程的数值解。提出了三个关于所提出算法的理论结果。首先，证明了迭代变量收敛到哈密顿-雅可比-伊萨亚斯方程的解。其次，实现了闭环系统的 L-增益性能。作为一个特例，标称系统的原点渐近稳定。第三，所得到的控制协议构成纳什均衡解。根据主要结果设计了基于神经网络的实现。最后，提供了两个数值示例来验证所提出方法的有效性。
