Neural network solution for finite-horizon H ∞ state feedback control of nonlinear systems

Abstract

In this article, neural networks are used to approximately solve the finite-horizon optimal H ∞ state feedback control problem. The method is based on solving a related Hamilton–Jacobi–Isaacs equation of the corresponding finite-horizon zero-sum game. The neural network approximates the corresponding game value function on a certain domain of the state-space and results in a control computed as the output of a neural network. It is shown that the neural network approximation converges uniformly to the game-value function and the resulting controller provides closed-loop stability and bounded L 2 gain. The result is a nearly exact H ∞ feedback controller with time-varying coefficients that is solved a priori offline. The results of this article are applied to the rotational/translational actuator benchmark nonlinear control problem.