Echo state network-based H∞ control for continuous-time nonlinear systems

In this paper, the Nash equilibrium strategy of the
$H_{\infty}$
control problem is designed for continuous-time nonlinear systems by utilizing a novel adaptive dynamic programming (ADP) method. The
$H_{\infty}$
control problem can be solved from the corresponding zero-sum game problem. In this task, a nonlinear partial differential Hamilton-Jacobi-Isaacs (HJI) equation is derived and is hard to be solved. A novel ADP method is designed to obtain the solution of the HJI equation. The echo state network (ESN) is utilized to approximate the critic function in the ADP method. The ESN can decrease the complexity of designing the structure of the hidden layer. A simulation is given to verify the availability of the novel ADP method.