On the Order Reduction Approach for Singularly Perturbed Optimal Control Systems

被引：0
|
作者：
Arie Leizarowitz
机构：
[1] Department of Mathematics,
[2] Technion,undefined
来源：
Set-Valued Analysis | 2002年 / 10卷
关键词：
singularly perturbed systems; order reduction approach; value function; variational limit problem; averaging technique;
D O I：
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中图分类号：
学科分类号：
摘要：
The order reduction method for singularly perturbed optimal control systems consists of employing the system obtained while setting the small parameter to be zero. In many situations the differential-algebraic system thus obtained indeed provides an appropriate approximation to the singularly perturbed problem with a small parameter. In this paper we establish that if relaxed controls are allowed then the answer to the question whether or not this method is valid depends essentially on one simple parameter: the dimension of the fast variable, denoted n. More specifically, if n=1 then the order reduction method is indeed applicable, while if n>1 then the set of singularly perturbed optimal control systems for which it is not applicable is dense (in the L∞ norm).
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页码：185 / 207
页数：22
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