一类几乎光滑控制的最优控制问题的计算方法

Ying Zhang, Zhaoyang Zhang, Yingtao Xu
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引用次数: 0

摘要

本文考虑一类包含连续控制和状态不等式约束的最优控制问题,其中控制几乎是光滑的。我们首先采用控制参数化技术,通过分段线性函数逼近控制信号。然后,我们开发了一种时间尺度变换程序,将近似问题转化为可以使用常规方法轻松求解的等效问题。在此基础上,构造了一种新的精确惩罚函数方法,在代价函数上附加惩罚约束违例。梯度公式和收敛性保证了转换后的无约束最优参数选择问题可以用现有的优化算法或软件包解决。最后通过算例验证了该方法的有效性和适用性。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
A Computational Approach to Optimal Control Problems with Almost Smooth Controls
In this paper, we consider a class of optimal control problems involving continuous control and state inequality constraints where the control is almost smooth. We first employ the control parametrization technique via approximating the control signal by a piecewise linear function. Then, we develop a time scaling transformation procedure for transforming the approximate problem into an equivalent problem that can be solved readily using conventional methods. On this basis, a novel exact penalty function method is constructed by appending penalized constraint violations to the cost function. The gradient formulas and convergent properties ensure that the transformed unconstrained optimal parameter selection problems can be solved by existing optimization algorithms or software packages. Finally, an example is solved showing the effectiveness and applicability of the approach proposed.
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