Symplectic Multi-Level Method for Solving Nonlinear Optimal Control Problem

PENG Hai-jun; GAO Qiang; WU Zhi-gang; ZHONG Wan-xie

doi:10.3879/j.issn.1000-0887.2010.10.006

Volume 31 Issue 10

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Article Navigation > Applied Mathematics and Mechanics > 2010 > 31(10): 1191-1200

PENG Hai-jun, GAO Qiang, WU Zhi-gang, ZHONG Wan-xie. Symplectic Multi-Level Method for Solving Nonlinear Optimal Control Problem[J]. Applied Mathematics and Mechanics, 2010, 31(10): 1191-1200. doi: 10.3879/j.issn.1000-0887.2010.10.006

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Symplectic Multi-Level Method for Solving Nonlinear Optimal Control Problem

doi: 10.3879/j.issn.1000-0887.2010.10.006

1.
Department of Engineering Mechanics, State Key Laboratory of Structural Analysis of Industrial Equipment, Dalian University of Technology, Dalian, Liaoning 116024, P. R. China;

Received Date: 1900-01-01
Rev Recd Date: 2010-08-30
Publish Date: 2010-10-15

Abstract

Abstract

The optimal control problem for nonlinear system was transformed into Hamiltonian system and a symplectic-preserving method was proposed.The state and costate variables were approximated by Lagrange polynomial and state variables at two ends of the time interval were taken as the independent variables, and then based on the dual variable principle, nonlinear optimal control problems were replaced by nonlinear equations.In the implement of symplectic algorithm, based on the 2^N algorithm, a multi-level method was proposed.When the time grid was refined from the low level to the high level, the initial state variables and costate variables of nonlinear equations could be obtained from Lagrange interpolation at the low level grid, which could improve the efficiency.Numerical simulations show the precision and efficiency of the proposed algorithm.
- nonlinear optimal control,
- dual variable,
- variational principle,
- multi-level iteration,
- symplectic algorithm

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References(14)

References

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