最优控制问题逼近下约束系统的柔性问题

IF 0.3 Q4 MATHEMATICS
A. Chernov
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引用次数: 0

摘要

对于具有函数等式约束的集总最优控制问题中控制函数的参数逼近得到的有限维数学规划问题(逼近问题),我们引入了约束系统的刚性和柔性的概念。对于给定可容许点的刚性,我们认为该点对于可容许集是孤立的;否则,在这一点上,我们称约束系统为灵活的。在利用二次指数函数(高斯函数)对控制函数进行参数逼近的情况下,在满足一些自然假设的前提下,证明了在逼近问题中,为了保证约束系统在给定容许点处的柔性,需要增加参数空间的维数。以月球软着陆问题为例,对我们的假设进行了检验。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
On flexibility of constraints system under approximation of optimal control problems
For finite-dimensional mathematical programming problems (approximating problems) being obtained by a parametric approximation of control functions in lumped optimal control problems with functional equality constraints, we introduce concepts of rigidity and flexibility for a system of constraints. The rigidity in a given admissible point is treated in the sense that this point is isolated for the admissible set; otherwise, we call a system of constraints as flexible in this point. Under using a parametric approximation for a control function with the help of quadratic exponentials (Gaussian functions) and subject to some natural hypotheses, we establish that in order to guarantee the flexibility of constraints system in a given admissible point it suffices to increase the dimension of parameter space in the approximating problem. A test of our hypotheses is illustrated by an example of the soft lunar landing problem.
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