$\mathbf{H}_{\infty}$ Preview Tracking Controller Based on Zero-Sum Game Theory

In this paper, a novel approach with preview information is proposed to solve the $H_{\infty}$ tracking problem for linear discrete-time systems. Based on core concepts from zero-sum game theory, a quadratic value function is derived to obtain the minimax preview controller using an algebraic Riccati equation. A new indicator called saddle-point bias is suggested to measure the degree of advantage of the two in the zero-sum game. The addition of preview information leads to a change in the saddlepoint bias, which indicates stronger noise suppression capability. Finally, a simulation example is provided to illustrate the effectiveness of the method presented in this study.