Controller Optimization for Multirate Systems Based on Reinforcement Learning

The goal of this paper is to design a model-free optimal controller for the multirate system based on reinforcement learning. Sampled-data control systems are widely used in the industrial production process and multirate sampling has attracted much attention in the study of the sampled-data control theory. In this paper, we assume the sampling periods for state variables are different from periods for system inputs. Under this condition, we can obtain an equivalent discrete-time system using the lifting technique. Then, we provide an algorithm to solve the linear quadratic regulator (LQR) control problem of multirate systems with the utilization of matrix substitutions. Based on a reinforcement learning method, we use online policy iteration and off-policy algorithms to optimize the controller for multirate systems. By using the least squares method, we convert the off-policy algorithm into a model-free reinforcement learning algorithm, which only requires the input and output data of the system. Finally, we use an example to illustrate the applicability and efficiency of the model-free algorithm above mentioned.