Optimal control laws for time-delay systems with saturating actuators based on heuristic dynamic programming

In this paper a new iterative heuristic dynamic programming (HDP) algorithm is proposed to solve the optimal control problem for a class of nonlinear discrete time-delay systems with saturating actuators. Considering the saturation nonlinearity in the actuators, a nonquadratic performance index function is introduced. In the meantime, a state modification is used to deal with the obstacle induced by time delays. In the new iterative HDP algorithm the local and global optimization searching processes are developed to solve the optimal feedback control problem with convergence analysis. In the presented iterative HDP algorithm, two neural networks are used to facilitate the implementation of the iterative algorithm. Finally, two simulation examples are given to demonstrate the convergence and feasibility of the proposed optimal control scheme.