Reachability Set

Leonid T. Ashchepkov (), Dmitriy V. Dolgy, Taekyun Kim and Ravi P. Agarwal
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Leonid T. Ashchepkov: Department of Mathematics, Institute of Mathematics and Computer Technologies, Far Eastern Federal University
Dmitriy V. Dolgy: Kwangwoon Glocal Education Center, Kwangwoon University, Department of Mathematics, Institute of Mathematics and Computer Technologies Far Eastern Federal University Vladivostok, Russia
Taekyun Kim: Kwangwoon University, Department of Mathematics
Ravi P. Agarwal: Texas A&M University - Kingsville, Mathematics

Chapter Chapter 3 in Optimal Control, 2021, pp 17-39 from Springer

Abstract: Abstract For the linear control systems it is proved Cauchy formula which represents the trajectory of the system with the help of the fundamental matrix. We list the properties of the fundamental matrix, introduce the notation of the reachability set of a linear system and establish its basic properties: the limitation, convexity, closure, and continuity. It is showed the relation of a special family of extreme controls with the boundary of a reachability set.

Date: 2021
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DOI: 10.1007/978-3-030-91029-7_3

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