Adaptive Dynamic Programming without Persistence Excitation for Tracking in A Special Class of Linear Systems with Input Constraints

In this paper, an approximate optimal control method with input constraints based on adaptive dynamic programming (ADP) is proposed for a class of special linear systems. The method is based on an actor/critic framework. The critic approximator is used to approximate the optimal cost function, and the actor approximator is used to approximate the bounded control input. In view of the fact that the algorithm requires a persistence of excitation (PE) condition, we use the previous data and the current data to alleviate this requirement. When Lyapunov method is used to prove stability, the error between the optimal control and the bounded control is considered. It is prove that the closed-loop system can be guaranteed to be uniformly ultimately bounded (UUB). On this basis, a robustness term is added to compensate the effect of the approximation error. A simulation example shows the effectiveness.