A solution to Hamilton-Jacobi equation and optimal feedback control law using neural networks

摘要

This paper is concerned with a state feedback controller using neural networks for nonlinear optimal regulator problem. Nonlinear optimal feedback control law can be synthesized by solving the Hamilton-Jacobi equation with three layered neural networks. The Hamilton-Jacobi equation generates the value function which is necessary for optimal controller synthesis. To obtain an approximate solution of the Hamilton-Jacobi equation, we solve an optimization problem which determines connection weights and thresholds in the neural networks. Gradient functions with respect to the connection weights and thresholds are calculated explicitly by the Lagrange multiplier method and used in the learning algorithm of the networks. We propose also a device by which an approximate solution to Hamilton-Jacobi equation converges to the true value function. The effectiveness of the proposed method was confirmed with simulations for various plants.