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

In this paper, we investigate the optimal control strategies for model-free zero-sum games involving the H(infinity )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.