Distributed Minmax Strategy for Multi-Agent Systems With Multiple Disturbances in Graphical Games

This paper studies the distributed minmax strategy of multi-agent systems with unknown multiple disturbances in graphical games over a network topology containing a directed spanning tree. Utilizing the sliding mode control technology and game-theoretical approaches, the distributed minmax strategy associated with the decoupled Hamilton-Jacobi-Isaacs equations are derived. To solve the strategy, an effective method based on reinforcement learning and neural network approximation is proposed in which the condition of persistent excitation is relaxed and the requirement of initial stabilizing control is removed. By Lyapunov stability theory, it is proven that under the proposed minmax strategy, the consensus error systems are asymptotically stable and the sliding mode dynamics exhibit <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\mathcal {L}_{2}$</tex-math></inline-formula>-gain stability. Finally, a numerical illustration is presented to demonstrate the effectiveness of the theoretical analysis.