Neuro-Optimal Trajectory Tracking With Value Iteration of Discrete-Time Nonlinear Dynamics

Abstract

In this article, a novel neuro-optimal tracking control approach is developed toward discrete-time nonlinear systems. By constructing a new augmented plant, the optimal trajectory tracking design is transformed into an optimal regulation problem. For discrete-time nonlinear dynamics, the steady control input corresponding to the reference trajectory is given. Then, the value-iteration-based tracking control algorithm is provided and the convergence of the value function sequence is established. Therein, the approximation error between the iterative value function and the optimal cost is estimated. The uniformly ultimately bounded stability of the closed-loop system is also discussed in detail. Moreover, the iterative heuristic dynamic programming (HDP) algorithm is implemented by involving the critic and action components, where some new updating rules of the action network are provided. Finally, two examples are used to demonstrate the optimality of the present controller as well as the effectiveness of the proposed method.