Neural networks for control
Approximate solutions to the time-invariant Hamilton-Jacobi-Bellman equation
Journal of Optimization Theory and Applications
Solving Hamilton-Jacobi-Bellman equations by a modified method of characteristics
Nonlinear Analysis: Theory, Methods & Applications - Lakshmikantham's Legacy: A tribute on his 75th birthday
Neural Network Control of Robot Manipulators and Nonlinear Systems
Neural Network Control of Robot Manipulators and Nonlinear Systems
Brief paper: A neural network solution for fixed-final time optimal control of nonlinear systems
Automatica (Journal of IFAC)
Automatica (Journal of IFAC)
Neural approximations for infinite-horizon optimal control of nonlinear stochastic systems
IEEE Transactions on Neural Networks
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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 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 article are applied to the rotational/translational actuator benchmark nonlinear control problem.