Singular perturbations in infinite-dimensional control systems

被引：17
|
作者：
Donchev, TD
Dontchev, AL
机构：
[1] Univ Architecture & Civil Engn, Dept Math, Sofia 1046, Bulgaria
[2] Math Reviews, Ann Arbor, MI 48107 USA
来源：
SIAM JOURNAL ON CONTROL AND OPTIMIZATION | 2003年 / 42卷 / 05期
关键词：
control systems; differential inclusions; singular perturbations; time scales; order reduction; convergence of solutions;
D O I：
10.1137/S0363012902416080
中图分类号：
TP [自动化技术、计算机技术];
学科分类号：
0812 ;
摘要：
In this paper, we consider a singularly perturbed control system involving differential inclusions in Banach spaces with slow and fast solutions. Using the averaging approach, we obtain sufficient conditions for the Hausdorff convergence of the set of slow solutions in the supremum norm. We present applications of the theorem to prove convergence of the fast solutions in terms of invariant measures and convergence of equi-Lipschitz solutions.
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页码：1795 / 1812
页数：18
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