Neural network solution for finite-horizon H∞ constrained optimal control of nonlinear systems

In this paper, neural networks are used to approximately solve the finite-horizon constrained input 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 by approximating the cost using a Neural Network. It is shown that the neural network approximation converges uniformly to the game-value function and the resulting nearly optimal constrained feedback controller provides closed-loop stability and bounded L_2/ gain. The result is a nearly optimal H_∞ feedback controller with time-varying coefficients that is solved a priori offline. The effectiveness of the method is shown on the rotational/translational actuator benchmark nonlinear control problem.