Dual iterative adaptive dynamic programming for a class of discrete-time nonlinear systems with time-delays

In this paper, a new dual iterative adaptive dynamic programming (ADP) algorithm is developed to solve optimal control problems for a class of nonlinear systems with time-delays in state and control variables. The idea is to use the dynamic programming theory to solve the expressions of the optimal performance index function and control. Then, the dual iterative ADP algorithm is introduced to obtain the optimal solutions iteratively, where in each iteration, the performance index function and the system states are both updated. Convergence analysis is presented to prove the performance index function to reach the optimum by the proposed method. Neural networks are used to approximate the performance index function and compute the optimal control policy, respectively, for facilitating the implementation of the dual iterative ADP algorithm. Simulation examples are given to demonstrate the validity of the proposed optimal control scheme.