A Nash Equilibrium in Multiplayer Zero-Sum Game with Completely Unknown Nonlinear System

The paper proposes an adaptive dynamic programming (ADP) algorithm for the multi <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$-H_{\infty}$</tex> control problem of the input-interference nonlinear system. First, it employs multiple inputs to counteract disturbance and defines nash equilibrium solutions for multiple <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$H_{\infty}$</tex> performance indices using multiplayer zero-sum game theory. Then, it utilizes neural networks to identify completely unknown systems and employs critic neural network learning for multiple <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$H_{\infty}$</tex> performance indices. Finally, the stability of the system is proved based on the Lyapunov method, and the effectiveness of the proposed method is verified through a simulation experiment.