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

Abstract

This paper provides necessary and sufficient conditions for the existence of the static output-feedback (OPFB) solution to the H <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</sub> control problem for linear discrete-time systems. It is shown that the solution of the static OPFB H <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</sub> control is a Nash equilibrium point. Furthermore, a Q-learning algorithm is developed to find the H <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</sub> 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.