Finite‐horizon Q‐learning for discrete‐time zero‐sum games with application to H∞$$ {H}_{\infty } $$ control

Abstract

AbstractIn this paper, we investigate the optimal control strategies for model‐free zero‐sum games involving the control. The key contribution is the development of a Q‐learning algorithm for linear quadratic games without knowing the system dynamics. The finite‐horizon setting is more practical than the infinite‐horizon setting, but it is difficult to solve the time‐varying Riccati equation associated with the finite‐horizon setting directly. The proposed algorithm is shown to solve the time‐varying Riccati equation iteratively without the use of models, and numerical experiments on aircraft dynamics demonstrate the algorithm's efficiency.