Gaussian Reinforcement Learning: Optimal Tracking Control for Uncertain Linear Systems

In this paper, a design method for PID control based on Gaussian reinforcement learning is proposed to find the optimal policy for linear quadratic tracking of an unknown system. Firstly, the mathematical model of the linear quadratic tracking problem with random disturbance is presented, and an analysis of the PID control structure is carried out. Secondly, a Gaussian model predictive control for the unknown model with random disturbances is provided. Finally, a Gaussian Q-learning method is given for the system based on this predictive model. The effectiveness of the proposed method is demonstrated through a numerical example.