Data-Driven Guaranteed Cost Control Design via Reinforcement Learning for Linear Systems With Parameter Uncertainties

Abstract

Controllers learned from data are more practical and promising than the existing model-based ones and their capability can be enhanced if a priori information about the controlled plant is available. Under this viewpoint, a data-driven guaranteed cost control (GCC) design is investigated for linear systems with time-varying parameter uncertainties. Initially, the GCC design is shown to be equivalent to an H <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</sub> state feedback control problem subject to a specific disturbance attenuation performance requirement. Then such an H <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</sub> control problem is regarded as a zero-sum game and reduces to seek the stabilizing solution of a parameterized algebraic Riccati equation (ARE). Furthermore, to solve the ARE approximately, a modified simultaneous policy update algorithm (SPUA) and the corresponding data-driven variant based on off-policy reinforcement learning (RL) and experience replay technique is proposed. Finally, a numerical simulation for aircrafts with harsh uncertainties is illustrated to validate the merits of the proposed methods.