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Applied Mathematics and Mechanics (English Edition) ›› 2010, Vol. 31 ›› Issue (10): 1251-1260.doi: https://doi.org/10.1007/s10483-010-1358-6

• Articles • 上一篇    下一篇

Symplectic multi-level method for solving nonlinear optimal control problem

彭海军1 高强1 吴志刚2 钟万勰1   

  1. 1. Department of Engineering Mechanics, State Key Laboratory of Structural Analysis of Industrial Equipment, Dalian University of Technology, Dalian 116024, Liaoning Province, P. R. China;
    2. School of Aeronautics and Astronautics, State Key Laboratory of Structural Analysis of Industrial Equipment, Dalian University of Technology, Dalian 116024, Liaoning Province, P. R. China
  • 收稿日期:2010-03-04 修回日期:2010-08-30 出版日期:2010-10-01 发布日期:2010-10-01

Symplectic multi-level method for solving nonlinear optimal control problem

PENG Hai-Jun1, GAO Qiang1, WU Zhi-Gang2, ZHONG Wan-Xie1   

  1. 1. Department of Engineering Mechanics, State Key Laboratory of Structural Analysis of Industrial Equipment, Dalian University of Technology, Dalian 116024, Liaoning Province, P. R. China;
    2. School of Aeronautics and Astronautics, State Key Laboratory of Structural Analysis of Industrial Equipment, Dalian University of Technology, Dalian 116024, Liaoning Province, P. R. China
  • Received:2010-03-04 Revised:2010-08-30 Online:2010-10-01 Published:2010-10-01

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1067

被引次数

11

摘要： By converting an optimal control problem for nonlinear systems to a Hamiltonian system, a symplecitc-preserving method is proposed. The state and costate variables are approximated by the Lagrange polynomial. The state variables at two ends of the time interval are taken as independent variables. Based on the dual variable principle, nonlinear optimal control problems are replaced with nonlinear equations. Furthermore, in the implementation of the symplectic algorithm, based on the 2N algorithm, a multilevel method is proposed. When the time grid is refined from low level to high level, the initial state and costate variables of the nonlinear equations can be obtained from the Lagrange interpolation at the low level grid to improve e±ciency. Numerical simulations show the precision and the e±ciency of the proposed algorithm in this paper.

Abstract: By converting an optimal control problem for nonlinear systems to a Hamiltonian system, a symplecitc-preserving method is proposed. The state and costate variables are approximated by the Lagrange polynomial. The state variables at two ends of the time interval are taken as independent variables. Based on the dual variable principle, nonlinear optimal control problems are replaced with nonlinear equations. Furthermore, in the implementation of the symplectic algorithm, based on the 2N algorithm, a multilevel method is proposed. When the time grid is refined from low level to high level, the initial state and costate variables of the nonlinear equations can be obtained from the Lagrange interpolation at the low level grid to improve e±ciency. Numerical simulations show the precision and the e±ciency of the proposed algorithm in this paper.

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