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.

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

• Rev Recd Date: 2007-01-07
• Publish Date: 2007-03-15
• 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.
•  [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. [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. [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

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