Optimal control for a class of nonlinear systems with state delay based on Adaptive Dynamic Programming with ε-error bound

In this paper, a finite-horizon ε-optimal control for a class of nonlinear systems with state delay is proposed by Adaptive Dynamic Programming (ADP) algorithm. First of all, the performance index function is defined and the Hamilton-Jacobi-Bellman (HJB) equation is obtained for the problem, the convergence of the iterative algorithm is also presented. Then, ADP algorithm for finite-horizon optimal control is introduced with an ε-error bound so as to get the ε-optimal control, and BP neural network is used to implement ADP algorithm. At last, an example is given to demonstrate the effectiveness of the proposed algorithm.