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

In this paper, 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 L₂ gain. The result is a nearly exact H_∞ feedback controller with time-varying coefficients that is solved a priori offline. The results of this paper are applied to the Rotational/Translational Actuator benchmark nonlinear control problem.