H∞ control of unknown discrete-time nonlinear systems with control constraints using adaptive dynamic programming

In this paper, we solve the H_∞ robust optimal control problem for discrete-time nonlinear systems with control saturation constraints using the iterative adaptive dynamic programming algorithm. First, a heuristic dynamic programming algorithm is derived to solve the Hamilton-Jacobi-Isaacs equation associated with the H_∞ control problem, and a convergence analysis is provided. Then, a dual heuristic dynamic programming algorithm with nonquadratic performance functional is developed to overcome the control saturation constraints. Finally, to facilitate the implementation of the algorithm, four neural networks are used to approximate the unknown nonlinear system, the control policy, the disturbance policy, and the value function.