Data-Driven Adaptive Optimal Control for Linear Systems with Structured Time-Varying Uncertainty

Abstract

In this paper, a data-driven adaptive optimal control strategy is proposed for a class of linear systems with structured time-varying uncertainty, minimizing the upper bound of a pre-defined cost function while maintaining the closed-loop stability. An off-policy data-driven reinforcement learning algorithm is presented, which uses repeatedly the online state signal on some fixed time intervals without knowing system information, yielding a guaranteed cost control (GCC) law with quadratic stability for the system. This law is further optimized through a particle swarm optimization (PSO) method, the parameters of which are adaptively adjusted by a fuzzy logic mechanism, and an optimal GCC law with the minimum upper bound of the cost function is finally obtained. The effectiveness of this strategy is verified on the dynamic model of a two-degree-of-freedom helicopter, showing that both stability and convergence of the closed-loop system are guaranteed and that the cost is minimized with much less iteration than the conventional PSO method with constant parameters.