Q-Learning for Finite-Horizon H∞ Tracking Control of Unknown Linear Discrete-Time Systems

In this paper, we present a Q-learning algorithm for finite-horizon H∞ tracking control of unknown linear discrete-time systems. Finite horizon control is challenging due to its correspondence with a time-varying Riccati equation. The proposed algorithm can determine the solution of the time-varying Riccati equation with unknown system dynamics. We first establish the time-varying Q-function, then propose a corresponding Q-learning algorithm and prove its convergence. Finally, the proposed algorithm is proved to be effective through numerical examples.