Linear Quadratic Tracker with Integrator using Integral Reinforcement Learning

This paper describes a Reinforcement Learning (RL) application using Linear Quadratic Regulator (LQR) based tracking controller, which is augmented with a tracking error term. In order to deal with the steady-state errors, Linear Quadratic Tracker with Integrator (LQTI) is designed by adding an integration term of the tracking error in the state variable. Based on the LQTI, an online learning using the Integral Reinforcement Learning (IRL) is applied for the tracking problem to find the optimal control on the partially unknown continuous-time systems by regulating the augmented state variable. The optimal control solution and the performance of the method are verified through numerical simulation on two applications.