Optimal control scheme for nonlinear systems with saturating actuator using ε-iterative adaptive dynamic programming

In this paper, a finite-horizon optimal control scheme for a class of nonlinear systems with saturating actuator is proposed by an improved iterative adaptive dynamic programming (ADP) algorithm. The Hamilton-Jacobi-Bellman (HJB) equation corresponding to constrained control is formulated using a suitable nonquadratic function. Then mathematical analysis of the convergence is presented, by proving that the performance index function can reach the optimum using the adaptive iteration. Finally the finite-horizon optimal control law can be obtained by the ε-iterative adaptive algorithm. The examples are given to demonstrate the effectiveness of the above methods.