Abstract

This work is concerned with the design of state-feedback, and static output-feedback con-trollers for uncertain discrete-time systems. The reinforcement learning (RL) method is employed and the controller to be designed is considered as an agent changing the behav-ior of the plant, which is the environment. A State-Action-Reward-State-Action (SARSA) algorithm is developed to achieve this goal. This is an open problem, as this offline design through the usage of RL is an approach not so well explored in the literature. The gain matrices are used directly as design variables in the SARSA algorithm, and a time -varying incremental step is employed. The method uses a grid in the uncertain parameters to place the poles of the closed-loop system in a disk on the complex plane. In addition, a stability test based on the Lyapunov theory is performed to provide a hard stability certifi-cate for the closed-loop system. Numerical experiments from the literature are used to illustrate the efficacy of the method, through the use of benchmark examples and exhaus-tive testing.(c) 2023 Elsevier Inc. All rights reserved.