The Adaptive Optimal Output Feedback Tracking Control of Unknown Discrete-Time Linear Systems Using a Multistep Q-Learning Approach

This paper investigates the output feedback (OPFB) tracking control problem for discrete-time linear (DTL) systems with unknown dynamics. To solve this problem, we use an augmented system approach, which first transforms the tracking control problem into a regulation problem with a discounted performance function. The solution to this problem is derived using a Bellman equation, based on the Q-function. In order to overcome the challenges of unmeasurable system state variables, we employ a multistep Q-learning algorithm that surpasses the advantages of the policy iteration (PI) and value iteration (VI) techniques and state reconstruction methods for output feedback control. As such, the requirement for an initial stabilizing control policy for the PI method is removed and the convergence speed of the learning algorithm is improved. Finally, we demonstrate the effectiveness of the proposed scheme using a simulation example.