This paper solves the robust tracking problem (RTP) for a type of
partially unknown nonlinear systems with asymmetric constrained-input by
utilizing an improved adaptive dynamic programming (ADP) method based on
experience replay (ER) technique and critic-only neural network (NN).
Initially, an identifier neural network (INN) is set to identify the
unknown parts of the system dynamics. Subsequently, the tracking error
and the desired trajectory are used to construct an augmented system, so
that the robust tracking problem (RTP) is transformed into a constrained
optimal control problem (OCP). It is proved that the designed control
policy of OCP can make the tracking error to be uniformly ultimately
bounded (UUB). Then, using the framework of ADP and critic-only NN to
solve the derived Hamilton-Jacobi-Bellman equation (HJBE). The NN weight
regulation law is partially derived by using gradient descent algorithm
(GDA) and then is improved by using the ER technique and the Lyapunov
stability theory, which no longer need the conditions of persistence of
excitation (PE) and initial admissible control. Besides, the total
system states and NN weights is proved to be closed stable by utilizing
the Lyapunov technique. Finally, through two simulation examples, it is
demonstrated that the proposed control scheme is effective.