| Numerical solutions of linear quadratic control for time-varying systems via symplectic conservative perturbation |
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| 作者姓名： | 谭述君 钟万勰 |
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| 作者单位： | State Key Laboratory of Structural Analysis for Industrial Equipment Dalian University of Technology，State Key Laboratory of Structural Analysis for Industrial Equipment，Dalian University of Technology，Dalian 116023，P.R.China，Dalian 116023，P.R.China |
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| 摘 要： | 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 is presented. It gives a uniform way to solve the linear quadratic control (LQ control) problems for linear time-varying systems accurately and efficiently, whose key points are solutions of differential Riccati equation (DRE) with variable coefficients and the state feedback equation. The method is symplectic conservative and has a good numerical stability and high precision. Numerical examples demonstrate the effectiveness of the proposed method.
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| 关 键 词： | 线性时变系统 线性二次控制 辛守衡摄动法 数值解 |
| 收稿时间： | 2006-05-31 |
| 修稿时间： | 2007-01-07 |
Numerical solutions of linear quadratic control for time-varying systems via symplectic conservative perturbation |
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| Tan?Shu-jun,Zhong?Wan-xie.Numerical solutions of linear quadratic control for time-varying systems via symplectic conservative perturbation[J].Applied Mathematics and Mechanics(English Edition),2007,28(3):277-287. |
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| Authors: | Tan Shu-jun Zhong Wan-xie |
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| Institution: | State Key Laboratory of Structural Analysis for Industrial Equipment,Dalian University of Technology,Dalian 116023,P.R.China |
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| 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 is presented. It gives a uniform way to solve the linear quadratic control (LQ control) problems for linear time-varying systems accurately and efficiently, whose key points are solutions of differential Riccati equation (DRE) with variable coefficients and the state feedback equation. The method is symplectic conservative and has a good numerical stability and high precision. Numerical examples demonstrate the effectiveness of the proposed method. |
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| Keywords: | linear time-varying systems linear quadratic control Riccati equation interval mixed energy state transition matrix symplectic conservative perturbation |
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