Numerical Solutions of LQ Control for Time-Varying Systems Via Symplectic Conservative Perturbation

TAN Shu-jun; ZHONG Wan-xie

Article Contents

Article Navigation > Applied Mathematics and Mechanics > 2007 > 28(3): 253-262

TAN Shu-jun, ZHONG Wan-xie. Numerical Solutions of LQ Control for Time-Varying Systems Via Symplectic Conservative Perturbation[J]. Applied Mathematics and Mechanics, 2007, 28(3): 253-262.

Citation:

TAN Shu-jun, ZHONG Wan-xie. Numerical Solutions of LQ Control for Time-Varying Systems Via Symplectic Conservative Perturbation[J]. Applied Mathematics and Mechanics, 2007, 28(3): 253-262.

Citation:

TAN Shu-jun, ZHONG Wan-xie. Numerical Solutions of LQ Control for Time-Varying Systems Via Symplectic Conservative Perturbation[J]. Applied Mathematics and Mechanics, 2007, 28(3): 253-262.

PDF( 413 KB)

Numerical Solutions of LQ Control for Time-Varying Systems Via Symplectic Conservative Perturbation

State Key Laboratory of Structural Analysis for Industrial Equipment, Dalian University of Technology, Dalian 116023, P. R. China

Received Date: 2006-09-26
Rev Recd Date: 2007-01-07
Publish Date: 2007-03-15

Abstract

Abstract

Optimal control system of state space is a conservative system,whose approximate method should be symplectic conservation.Based on the precise integration method,an algorithm of symplectic conservative perturbation was presented.It gives a uniform way to solve the LQ control problems for linear time-varying systems accurately and efficiently,whose key points are solutions of differential Riccati equation and the state feedback equation with variable coefficient.The method is symplectic conservative and has a good numerical stability and high precision.Numerical examples demonstrate the effectiveness of the proposed method.
- linear time-varying system,
- LQ control,
- Riccati equation with variable coefficient,
- interval mixed energy,
- state transition matrix,
- symplectic conservative perturbation

FullText(HTML)

References(13)

References

[1]	Anderson Brian D O,Moore John B.Optimal Control: Quadratic Methods[M].Englewood Cliffs,N J:Prentice Hall,1990.
[2]	Chen C T.Linear System Theory and Design[M].New York:CBS College,1984.
[3]	Chen W L,Shih Y P.Analysis and optimal control of time-varying linear systems via Walsh functions[J].Int J Control,1978,27(6):917-932. doi: 10.1080/00207177808922422
[4]	徐宁寿,郑兵.方块脉冲函数用于线性时变系统的分析和最优控制[J].自动化学报,1982,8(1):55-67.
[5]	古天龙,徐国华. 分段线性函数用于时变系统的最优控制[J].控制理论与应用,1989,6(4):102-108.
[6]	Hsiao C H,Wang W J.Optimal control of linear time-varying systems via Haar wavelets[J].Journal of Optimization Theory and Applications,1999,103(4):641-655. doi: 10.1023/A:1021740209084
[7]	钟万勰. 计算结构力学与最优控制[M].大连:大连理工大学出版社，1993.
[8]	钟万勰. 线性二次最优控制的精细积分[J]. 自动化学报,2002,27(2):166-173.
[9]	钟万勰,姚征.时间有限元与保辛[J].机械强度,2005,27(2):178-183.
[10]	钟万勰. 应用力学的辛数学方法[M].北京:高等教育出版社, 2006.
[11]	ZHONG Wan-xie.Duality System in Applied Mechanics and Optimal Control[M].New York: Kluwer Academic Publishers, 2004.
[12]	Choi Chiu H.Time-varying Riccati differential equation for numerical experiments[A].Proceedings of the 29th Conference on Decision and Control[C]. Honolulu, Hawaii:Dec. 1990, 930-940.
[13]	LU Ping. Closed-form control laws for linear time-varying systems[J].IEEE Transaction on Automatic Control,2000,45(3):537-542. doi: 10.1109/9.847739