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求解最优控制问题的Chebyshev-Gauss伪谱法

唐小军 尉建利 陈凯

唐小军, 尉建利, 陈凯. 求解最优控制问题的Chebyshev-Gauss伪谱法. 自动化学报, 2015, 41(10): 1778-1787. doi: 10.16383/j.aas.2015.e130297
引用本文: 唐小军, 尉建利, 陈凯. 求解最优控制问题的Chebyshev-Gauss伪谱法. 自动化学报, 2015, 41(10): 1778-1787. doi: 10.16383/j.aas.2015.e130297
TANG Xiao-Jun, WEI Jian-Li, CHEN Kai. A Chebyshev-Gauss Pseudospectral Method for Solving Optimal Control Problems. ACTA AUTOMATICA SINICA, 2015, 41(10): 1778-1787. doi: 10.16383/j.aas.2015.e130297
Citation: TANG Xiao-Jun, WEI Jian-Li, CHEN Kai. A Chebyshev-Gauss Pseudospectral Method for Solving Optimal Control Problems. ACTA AUTOMATICA SINICA, 2015, 41(10): 1778-1787. doi: 10.16383/j.aas.2015.e130297

求解最优控制问题的Chebyshev-Gauss伪谱法

doi: 10.16383/j.aas.2015.e130297
基金项目: 

Supported by Natural Science Basic Research Plan in Shaanxi Province of China (2014JQ8366), Fundamental Research Foun- dation of Northwestern Polytechnical University (JC20120210, JC20110238), and Aeronautical Science Foundation of China (20120853007)

A Chebyshev-Gauss Pseudospectral Method for Solving Optimal Control Problems

Funds: 

Supported by Natural Science Basic Research Plan in Shaanxi Province of China (2014JQ8366), Fundamental Research Foun- dation of Northwestern Polytechnical University (JC20120210, JC20110238), and Aeronautical Science Foundation of China (20120853007)

  • 摘要: 提出了一种求解最优控制问题的Chebyshev-Gauss伪谱法, 配点选择为Chebyshev-Gauss点. 通过比较非线性规划问题的Kaursh-Kuhn-Tucker条件和伪谱离散化的最优性条件, 导出了协态和Lagrange乘子的估计公式. 在状态逼近中, 采用了重心Lagrange插值公式, 并提出了一种简单有效的计算状态伪谱微分矩阵的方法. 该法的独特优势是具有良好的数值稳定性和计算效率. 仿真结果表明, 该法能够高精度地求解带有约束的复杂最优控制问题.
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出版历程
  • 收稿日期:  2013-12-18
  • 修回日期:  2014-05-28
  • 刊出日期:  2015-10-20

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