Precise Integration Method for Solving Noncooperative LQ Differential Game
The key of solving the noncooperative linear quadratic (LQ) differential game is to solve the coupled matrix Riccati differential equation. The precise integration method based on the adaptive choosing of the two parameters is expanded from the traditional symmetric Riccati differential equation to...
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Hindawi Limited
2013-01-01
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Series: | Mathematical Problems in Engineering |
Online Access: | http://dx.doi.org/10.1155/2013/713725 |
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doaj-7aedb63119e742e4abbdafef1e93260c2020-11-24T20:57:52ZengHindawi LimitedMathematical Problems in Engineering1024-123X1563-51472013-01-01201310.1155/2013/713725713725Precise Integration Method for Solving Noncooperative LQ Differential GameHai-Jun Peng0Sheng Zhang1Zhi-Gang Wu2Biao-Song Chen3Department of Engineering Mechanics, State Key Laboratory of Structural Analysis of Industrial Equipment, Dalian University of Technology, Dalian 116024, ChinaDepartment of Engineering Mechanics, State Key Laboratory of Structural Analysis of Industrial Equipment, Dalian University of Technology, Dalian 116024, ChinaSchool of Aeronautics and Astronautics, State Key Laboratory of Structural Analysis of Industrial Equipment, Dalian University of Technology, Dalian 116024, ChinaDepartment of Engineering Mechanics, State Key Laboratory of Structural Analysis of Industrial Equipment, Dalian University of Technology, Dalian 116024, ChinaThe key of solving the noncooperative linear quadratic (LQ) differential game is to solve the coupled matrix Riccati differential equation. The precise integration method based on the adaptive choosing of the two parameters is expanded from the traditional symmetric Riccati differential equation to the coupled asymmetric Riccati differential equation in this paper. The proposed expanded precise integration method can overcome the difficulty of the singularity point and the ill-conditioned matrix in the solving of coupled asymmetric Riccati differential equation. The numerical examples show that the expanded precise integration method gives more stable and accurate numerical results than the “direct integration method” and the “linear transformation method”.http://dx.doi.org/10.1155/2013/713725 |
collection |
DOAJ |
language |
English |
format |
Article |
sources |
DOAJ |
author |
Hai-Jun Peng Sheng Zhang Zhi-Gang Wu Biao-Song Chen |
spellingShingle |
Hai-Jun Peng Sheng Zhang Zhi-Gang Wu Biao-Song Chen Precise Integration Method for Solving Noncooperative LQ Differential Game Mathematical Problems in Engineering |
author_facet |
Hai-Jun Peng Sheng Zhang Zhi-Gang Wu Biao-Song Chen |
author_sort |
Hai-Jun Peng |
title |
Precise Integration Method for Solving Noncooperative LQ Differential Game |
title_short |
Precise Integration Method for Solving Noncooperative LQ Differential Game |
title_full |
Precise Integration Method for Solving Noncooperative LQ Differential Game |
title_fullStr |
Precise Integration Method for Solving Noncooperative LQ Differential Game |
title_full_unstemmed |
Precise Integration Method for Solving Noncooperative LQ Differential Game |
title_sort |
precise integration method for solving noncooperative lq differential game |
publisher |
Hindawi Limited |
series |
Mathematical Problems in Engineering |
issn |
1024-123X 1563-5147 |
publishDate |
2013-01-01 |
description |
The key of solving the noncooperative linear quadratic (LQ) differential game is to solve the coupled matrix Riccati differential equation. The precise integration method based on the adaptive choosing of the two parameters is expanded from the traditional symmetric Riccati differential equation to the coupled asymmetric Riccati differential equation in this paper. The proposed expanded precise integration method can overcome the difficulty of the singularity point and the ill-conditioned matrix in the solving of coupled asymmetric Riccati differential equation. The numerical examples show that the expanded precise integration method gives more stable and accurate numerical results than the “direct integration method” and the “linear transformation method”. |
url |
http://dx.doi.org/10.1155/2013/713725 |
work_keys_str_mv |
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_version_ |
1716787301411979264 |