IEICE TRANSACTIONS on Fundamentals
Approximate Solution of Hamilton-Jacobi-Bellman Equation by Using Neural Networks and Matrix Calculus Techniques
Summary :
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.
- Publication
- IEICE TRANSACTIONS on Fundamentals Vol.E84-A No.6 pp.1549-1556
- Publication Date
- 2001/06/01
- Publicized
- Online ISSN
- DOI
- Type of Manuscript
- PAPER
- Category
- Systems and Control
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Xu WANG, Kiyotaka SHIMIZU, "Approximate Solution of Hamilton-Jacobi-Bellman Equation by Using Neural Networks and Matrix Calculus Techniques" in IEICE TRANSACTIONS on Fundamentals,
vol. E84-A, no. 6, pp. 1549-1556, June 2001, doi: .
Abstract: 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.
URL: https://global.ieice.org/en_transactions/fundamentals/10.1587/e84-a_6_1549/_p
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@ARTICLE{e84-a_6_1549,
author={Xu WANG, Kiyotaka SHIMIZU, },
journal={IEICE TRANSACTIONS on Fundamentals},
title={Approximate Solution of Hamilton-Jacobi-Bellman Equation by Using Neural Networks and Matrix Calculus Techniques},
year={2001},
volume={E84-A},
number={6},
pages={1549-1556},
abstract={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.},
keywords={},
doi={},
ISSN={},
month={June},}
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TY - JOUR
TI - Approximate Solution of Hamilton-Jacobi-Bellman Equation by Using Neural Networks and Matrix Calculus Techniques
T2 - IEICE TRANSACTIONS on Fundamentals
SP - 1549
EP - 1556
AU - Xu WANG
AU - Kiyotaka SHIMIZU
PY - 2001
DO -
JO - IEICE TRANSACTIONS on Fundamentals
SN -
VL - E84-A
IS - 6
JA - IEICE TRANSACTIONS on Fundamentals
Y1 - June 2001
AB - 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.
ER -
English
