New smoothing techniques for solving bang-bang optimal control problems——numerical results and statistical interpretation

R. Bertrand; R. Epenoy

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New smoothing techniques for solving bang-bang optimal control problems——numerical results and statistical interpretation

机译：解决bang-bang最优控制问题的新平滑技术-数值结果与统计解释

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In this paper, we investigate the solution of bang-bang optimal control problems by shooting methods. We will show how modifying the performance index by a term depending on a small parameter ε yields more regular controls and shooting functions. A continuation procedure on ε will lead us to a good approximation of the initial solution. Then, a statistical interpretation of the method is given, providing us with a general framework for building new regular controls. Finally, two numerical examples are solved illustrating the interest of our method.

机译：在本文中，我们研究了通过射击方法来解决bang-bang最优控制问题。我们将展示如何根据一个小的参数ε来用术语修改性能指标，从而产生更多常规控件和射击功能。 ε上的延续过程将使我们对初始解有一个很好的近似。然后，对该方法进行了统计解释，为我们提供了用于构建新常规控件的通用框架。最后，解决了两个数值示例，说明了我们方法的重要性。

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来源
《Optimal Control Applications and Methods》 |2002年第4期|共27页
作者
R. Bertrand; R. Epenoy;
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原文格式 PDF
正文语种 eng
中图分类应用数学;
关键词
Bang-bang optimal control; Smoothing methods; Shooting methods; Low-thrust; Interplanetary missions;

机译：Bang-bang最优控制;平滑方法;射击方法;低推力;星际任务;

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1. New smoothing techniques for solving bang-bang optimal control problems——numerical results and statistical interpretation [J] . R. Bertrand, R. Epenoy Optimal Control Applications and Methods . 2002,第4期

机译：解决bang-bang最优控制问题的新平滑技术-数值结果与统计解释
2. A modified control parametrization method for the numerical solution of bang-bang optimal control problems [J] . Mehrpouya Mohammad Ali, Fallahi Shirin Journal of vibration and control: JVC . 2015,第12期

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3. Numerical approximation of bang-bang controls for the heat equation: An optimal design approach [J] . Münch A., Periago F. Systems and Control Letters . 2013,第8期

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4. Mesh Refinement Method for Solving Bang-Bang Optimal Control Problems Using Direct Collocation [C] . Yunus M. Agamawi, William W. Hager, Anil V. Rao AIAA SciTech forum and exposition . 2020

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5. Development and use of statistical process control (SPC) techniques for real-time interpretation of wastewater treatment plant data. [D] . Sweeney, Michael William. 1990

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7. Numerical approximation of bang-bang controls for the heat equation: an optimal design approach [O] . Francisco Periago 2013

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New smoothing techniques for solving bang-bang optimal control problems——numerical results and statistical interpretation

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