Approximate Solution of Hamilton-Jacobi-Bellman Equation by Using Neural Networks and Matrix Calculus Techniques

Xu WANG  Kiyotaka SHIMIZU  

IEICE TRANSACTIONS on Fundamentals of Electronics, Communications and Computer Sciences   Vol.E84-A   No.6   pp.1549-1556
Publication Date: 2001/06/01
Online ISSN: 
Print ISSN: 0916-8508
Type of Manuscript: PAPER
Category: Systems and Control
Hamilton-Jacobi-Bellman equation,  neural network,  optimal control,  nonlinear control,  state feedback control,  

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In this paper we propose a new algorithm to approximate the solution of Hamilton-Jacobi-Bellman equation by using a three layer neural network for affine and general nonlinear systems, and the state feedback controller can be obtained which make the closed-loop systems be suboptimal within a restrictive training domain. Matrix calculus theory is used to get the gradients of training error with respect to the weight parameter matrices in neural networks. By using pattern mode learning algorithm, many examples show the effectiveness of the proposed method.