Multi-H∞ Controls for Unknown Input-Interference Nonlinear System With Reinforcement Learning

This article studies the multi-
$\text{H}\infty $
controls for the input-interference nonlinear systems via adaptive dynamic programming (ADP) method, which allows for multiple inputs to have the individual selfish component of the strategy to resist weighted interference. In this line, the ADP scheme is used to learn the Nash-optimization solutions of the input-interference nonlinear system such that multiple
$\text{H}\infty $
performance indices can reach the defined Nash equilibrium. First, the input-interference nonlinear system is given and the Nash equilibrium is defined. An adaptive neural network (NN) observer is introduced to identify the input-interference nonlinear dynamics. Then, the critic NNs are used to learn the multiple
$\text{H}\infty $
performance indices. A novel adaptive law is designed to update the critic NN weights by minimizing the Hamiltonian–Jacobi–Isaacs (HJI) equation, which can be used to directly calculate the multi-
$\text{H}\infty $
controls effectively by using input–output data such that the actor structure is avoided. Moreover, the control system stability and updated parameter convergence are proved. Finally, two numerical examples are simulated to verify the proposed ADP scheme for the input-interference nonlinear system.