非线性最优控制问题的保辛多层次求解方法

彭海军; 高强; 吴志刚; 钟万勰

doi:10.3879/j.issn.1000-0887.2010.10.006

非线性最优控制问题的保辛多层次求解方法

doi: 10.3879/j.issn.1000-0887.2010.10.006

1.
大连理工大学工程力学系,工业装备结构分析国家重点实验室,辽宁大连116024;2.大连理工大学航空航天学院,工业装备结构分析国家重点实验室,辽宁大连116024

基金项目: 国家自然科学基金资助项目(10632030;10902020;10721062);高等学校博士点基金资助项目(20070141067);辽宁省博士启动基金资助项目(20081091);辽宁省重点实验室资助项目(2009S018)

详细信息

作者简介:
彭海军(1982- ),男,河北邯郸人,博士生(Tel:+86-411-84706574;E-mail:hjpeng@dlut.edu.cn);高强(1978- ),男,内蒙古赤峰人,讲师,博士(联系人.Tel:+86-411-84707608;E-mail:qgao@dlut.edu.cn).

中图分类号: O231.2;O241.81
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- 被引次数: 0
出版历程
- 收稿日期: 1900-01-01
- 修回日期: 2010-08-30
- 刊出日期: 2010-10-15

Symplectic Multi-Level Method for Solving Nonlinear Optimal Control Problem

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

摘要

摘要: 将非线性系统的最优控制问题导向Hamilton系统，提出了求解非线性最优控制问题的保辛多层次方法．首先，以时间区段两端状态为独立变量并在区段内采用Lagrange插值近似状态和协态变量，通过对偶变量变分原理将非线性最优控制问题转化为非线性方程组的求解．然后，在保辛算法的具体实施过程中提出了多层次求解思想，以2N类算法为基础由低层次到高层次加密离散时间区段，利用Lagrange插值得到网格加密后的初始状态与协态变量作为求解非线性方程组的初值，可提高计算效率．数值算例验证了算法在求解效率与求解精度上的有效性．
- 非线性最优控制 /
- 对偶变量 /
- 变分原理 /
- 多层次迭代 /
- 保辛
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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参考文献(14)

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