Parametric variational solution of linear-quadratic optimal control problems with control inequality constraints

doi:10.1007/s10483-014-1858-6

Applied Mathematics and Mechanics (English Edition) ›› 2014, Vol. 35 ›› Issue (9): 1079-1098.doi: https://doi.org/10.1007/s10483-014-1858-6

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Parametric variational solution of linear-quadratic optimal control problems with control inequality constraints

彭海军¹, 高强¹, 张洪武¹, 吴志刚², 钟万勰¹

1. State Key Laboratory of Structural Analysis for Industrial Equipment, Department of Engineering Mechanics, Dalian University of Technology, Dalian 116024, Liaoning Province, P. R. China;
2. State Key Laboratory of Structural Analysis for Industrial Equipment, School of Aeronautics and Astronautics, Dalian University of Technology, Dalian 116024, Liaoning Province, P. R. China

收稿日期:2013-09-06 修回日期:2014-02-19 出版日期:2014-09-01 发布日期:2014-09-01
通讯作者: Qiang GAO, qgao@dlut.edu.cn E-mail:qgao@dlut.edu.cn
基金资助:
Project supported by the National Natural Science Foundation of China (Nos. 11102031 and 11272076), the Fundamental Research Funds for Central Universities (No.DUT13LK25), the Key Laboratory Fund of Liaoning Province (No. L2013015), the China Postdoctoral Science Foundation (No. 2014M550155), and the State Key Laboratory of Mechanics and Control of Mechanical Structures (Nanjing University of Aeronautics and Astronautics) (No.MCMS-0114G02)

Parametric variational solution of linear-quadratic optimal control problems with control inequality constraints

Hai-jun PENG¹, Qiang GAO¹, Hong-wu ZHANG¹, Zhi-gang WU², Wan-xie ZHONG¹

1. State Key Laboratory of Structural Analysis for Industrial Equipment, Department of Engineering Mechanics, Dalian University of Technology, Dalian 116024, Liaoning Province, P. R. China;
2. State Key Laboratory of Structural Analysis for Industrial Equipment, School of Aeronautics and Astronautics, Dalian University of Technology, Dalian 116024, Liaoning Province, P. R. China

Received:2013-09-06 Revised:2014-02-19 Online:2014-09-01 Published:2014-09-01
Supported by:
Project supported by the National Natural Science Foundation of China (Nos. 11102031 and 11272076), the Fundamental Research Funds for Central Universities (No.DUT13LK25), the Key Laboratory Fund of Liaoning Province (No. L2013015), the China Postdoctoral Science Foundation (No. 2014M550155), and the State Key Laboratory of Mechanics and Control of Mechanical Structures (Nanjing University of Aeronautics and Astronautics) (No.MCMS-0114G02)

摘要/Abstract

摘要： A parametric variational principle and the corresponding numerical algorithm are proposed to solve a linear-quadratic (LQ) optimal control problem with control inequality constraints. Based on the parametric variational principle, this control problem is transformed into a set of Hamiltonian canonical equations coupled with the linear complementarity equations, which are solved by a linear complementarity solver in the discrete-time domain. The costate variable information is also evaluated by the proposed method. The parametric variational algorithm proposed in this paper is suitable for both time-invariant and time-varying systems. Two numerical examples are used to test the validity of the proposed method. The proposed algorithm is used to astrodynamics to solve a practical optimal control problem for rendezvousing spacecrafts with a finite low thrust. The numerical simulations show that the parametric variational algorithm is effective for LQ optimal control problems with control inequality constraints.

关键词: optimal control, linear complementarity, linear-quadratic (LQ), astrodynamics, parametric variational principle, inequality constraint

Abstract: A parametric variational principle and the corresponding numerical algorithm are proposed to solve a linear-quadratic (LQ) optimal control problem with control inequality constraints. Based on the parametric variational principle, this control problem is transformed into a set of Hamiltonian canonical equations coupled with the linear complementarity equations, which are solved by a linear complementarity solver in the discrete-time domain. The costate variable information is also evaluated by the proposed method. The parametric variational algorithm proposed in this paper is suitable for both time-invariant and time-varying systems. Two numerical examples are used to test the validity of the proposed method. The proposed algorithm is used to astrodynamics to solve a practical optimal control problem for rendezvousing spacecrafts with a finite low thrust. The numerical simulations show that the parametric variational algorithm is effective for LQ optimal control problems with control inequality constraints.

Key words: linear-quadratic (LQ), inequality constraint, parametric variational principle, linear complementarity, astrodynamics, optimal control

中图分类号:

彭海军;高强;张洪武;吴志刚;钟万勰. Parametric variational solution of linear-quadratic optimal control problems with control inequality constraints[J]. Applied Mathematics and Mechanics (English Edition), 2014, 35(9): 1079-1098.

Hai-jun PENG;Qiang GAO;Hong-wu ZHANG;Zhi-gang WU;Wan-xie ZHONG. Parametric variational solution of linear-quadratic optimal control problems with control inequality constraints[J]. Applied Mathematics and Mechanics (English Edition), 2014, 35(9): 1079-1098.

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Parametric variational solution of linear-quadratic optimal control problems with control inequality constraints

Parametric variational solution of linear-quadratic optimal control problems with control inequality constraints

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