NDLI: Toward Applications of Linear Control Systems on the Real World and Theoretical Challenges

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Toward Applications of Linear Control Systems on the Real World and Theoretical Challenges

Content Provider	MDPI
Author	Ayala, Víctor Torreblanca, María Valdivia, William
Copyright Year	2021
Description	Many significant real world challenges arise as optimization problems on different classes of control systems. In particular, ordinary differential equations with symmetries. The purpose of this review article is twofold. First, we give the information we have about the class of Linear Control Systems $ΣG$ on a low dimension matrix Lie group G. Second, we invite the Mathematical community to consider possible applications through the Pontryagin Maximum Principle for $ΣG$ . In addition, we challenge some theoretical open problems. The class $ΣG$ is a perfect generalization of the classical Linear Control System on the Abelian group $Rn$ . Let G be a Lie group of dimension two or three. Related to $ΣG$ , this review describes the actual results about controllability, the time-optimal Hamiltonian equations and, the Pontryagin Maximum Principle. We show how to build $ΣG$ , through several examples on low dimensional matrix groups.
Starting Page	167
e-ISSN	20738994
DOI	10.3390/sym13020167
Journal	Symmetry
Issue Number	2
Volume Number	13
Language	English
Publisher	MDPI
Publisher Date	2021-01-22
Access Restriction	Open
Subject Keyword	Symmetry Automotive Engineering Linear Control Systems Matrix Lie Groups Controllability Pontryagin Maximum Principle
Content Type	Text
Resource Type	Article

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