Model-Free $H_{2}/H_{\infty}$ Predictive Control for Discrete-Time System via Q-Learning

This paper presents a model-free
$H_{2}/H_{\infty}$
Q-learning predictive control strategy for linear discrete-time systems. To design predictive controller with the system measured states, a policy iteration solution algorithm is employed to approximate the control inputs. Specifically, the developed algorithm is formulated in the form of linear matrix inequalities, designed to stabilize the system with mixed
$H_{2}/H_{\infty}$
control performance. Additionally, to improve robust performance under system disturbance variations, we introduce the receding horizon optimization into the Q-learning based predictive control. Finally, simulation results demonstrate the effectiveness of the proposed approach.