Neural network-based online H∞ control for discrete-time affine nonlinear system using adaptive dynamic programming

In this paper, the problem of H∞H∞ control design for affine nonlinear discrete-time systems is addressed by using adaptive dynamic programming (ADP). First, the nonlinear H∞H∞ control problem is transformed into solving the two-player zero-sum differential game problem of the nonlinear system. Then, the critic, action and disturbance networks are designed by using neural networks to solve online the Hamilton–Jacobi–Isaacs (HJI) equation associating with the two-player zero-sum differential game. When novel weight update laws for the critic, action and disturbance networks are tuned online by using data generated in real-time along the system trajectories, it is shown that the system states, all neural networks weight estimation errors are uniformly ultimately bounded by using Lyapunov techniques. Further, it is shown that the output of the action network approaches the optimal control input with small bounded error and the output of the disturbance network approaches the worst disturbance with small bounded error. At last, simulation results are presented to demonstrate the effectiveness of the new ADP-based method.