Distributed Global Nash Containment Control and Learning of Multiplayer Multiagent Systems

This paper studies multiplayer multiagent differential graphical games, where each agent represents a linear dynamic system with multiple heterogeneous control inputs, referred to as players. The objective of the games is to control all followers to achieve containment within the convex hull of the leaders. Meanwhile, each player minimizes its cost function, which is also jointly affected by the other players and neighboring states in the same and neighboring agents. We design global Nash equilibrium (NE) (called Nash) control policies in the games, enabling all players to play the optimal control policies. The global Nash control solution is ensured to be distributed as it is computed using only local agents’ states. The solvability of the games, the asymptotic stability of the local error system, and the distributed global NE property are guaranteed. In addition, a data-driven integral reinforcement learning (RL) algorithm ensures the online computation of the distributed Nash control without requiring explicit knowledge of the system model matrices, by utilizing online measurements of system trajectories. The algorithm solves optimal control and inverse optimal control (IOC) as subproblems. A simulation example validates the algorithms.