The rate of convergence for a pseudospectral optimal control method
The rate of convergence for a pseudospectral optimal control method
复制标题
伪谱最优控制方法的收敛速度
DOI：
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发表时间：
2008
期刊：
影响因子：
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通讯作者：
W. Kang
中科院分区：
文献类型：
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作者：
W. Kang
在过去的十年中，伪谱（PS）方法已成为非线性约束最优控制问题的流行计算解决方案。它们已被应用于许多工业强度的问题，特别是美国宇航局最近对国际空间站进行的零推进剂操纵。在本文中，我们证明了使用 PS 方法计算的近似最优成本的收敛速度定理。本文与现有关于 PS 最优控制以及其他一些直接计算方法的论文有几个本质区别。首先，证明没有使用最优控制的必要条件。其次，我们不做矫顽力类型的假设。因此，该理论不需要最优解的局部唯一性。该证明不是建立在一致性近似理论的基础上的。因此，我们可以删除之前关于 PS 最优控制方法的结果中的一些限制性假设。
Over the last decade, pseudospectral (PS) methods have emerged as a popular computational solution for the problem of nonlinear constrained optimal control. They have been applied to many industrial-strength problems, notably the recent zero-propellant-maneuvering of the International Space Station performed by NASA. In this paper, we prove a theorem on the rate of convergence for the approximate optimal cost computed using PS methods. This paper contains several essential differences from existing papers on PS optimal control as well as some other direct computational methods. First, the proofs do not use necessary conditions of optimal control. Secondly, we do not make coercivity type of assumptions. As a result, the theory does not require the local uniqueness of optimal solutions. The proof is not build on the bases of consistency approximation theory. Thus, we can remove some restrictive assumptions in the previous results on PS optimal control methods.