Improved and Stable Data-Based Tracking Control via Approximate Iterative Q-Learning

In this paper, to avoid computing the feedward control input and to completely eliminate the tracking error, an improved cost function with respect to the tracking error is proposed, under which the optimal tracking controller can stabilize the tracking error system. Then, the approximate value-iteration-based Q-learning is given to solve the neuro-optimal control policy. Also, the finite error bound of the approximate Q-function is established. In addition, for guaranteeing the admissibility of the obtained control policies, some stability conditions for this data-based iterative Q-learning are developed. When the stability conditions are satisfied, it is ensured that the iterative control policies derived from the critic network and the trained action network with approximation errors will stabilize the tracking error system. Finally, a simulation example is employed to implement the data-based Q-learning algorithm and verify the present theoretical results.