H∞ Tracking Control for Linear Discrete-Time Systems: Model-Free Q-Learning Designs

In this letter, a novel model-free Q-learning based approach is developed to solve the
$H\infty $
tracking problem for linear discrete-time systems. A new exponential discounted value function is introduced that includes the cost of the whole control input and tracking error. The tracking Bellman equation and the game algebraic Riccati equation (GARE) are derived. The solution to the GARE leads to the feedback and feedforward parts of the control input. A Q-learning algorithm is then developed to learn the solution of the GARE online without requiring any knowledge of the system dynamics. Convergence of the algorithm is analyzed, and it is also proved that probing noises in maintaining the persistence of excitation (PE) condition do not result in any bias. An example of the F-16 aircraft short period dynamics is developed to validate the proposed algorithm.