$H_{\infty}$ Static Output-Feedback Control Design for Discrete-Time Systems Using Reinforcement Learning

This paper provides necessary and sufficient conditions for the existence of the static output-feedback (OPFB) solution to the H
_∞
control problem for linear discrete-time systems. It is shown that the solution of the static OPFB H
_∞
control is a Nash equilibrium point. Furthermore, a Q-learning algorithm is developed to find the H
_∞
OPFB solution online using data measured along the system trajectories and without knowing the system matrices. This is achieved by solving a game algebraic Riccati equation online and using the measured data. A simulation example shows the effectiveness of the proposed method.