The General Solution for Affine Control Systems on Lie Groups

The purpose of this paper is to present explicitly the solution curve for commutative affine control systems on Lie groups under the assumption that the automorphisms associated with the linear vector fields commutes. If we assume that the derivations associated with the linear vector fields of the...

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Bibliographic Details
Published inJournal of dynamical and control systems Vol. 28; no. 2; pp. 423 - 437
Main Authors de Oliveira, João Paulo Lima, Santana, Alexandre J., Stelmastchuk, Simão N.
Format Journal Article
LanguageEnglish
Published New York Springer US 01.04.2022
Springer Nature B.V
Subjects
Automorphisms
Calculus of Variations and Optimal Control; Optimization
Conjugation
Control
Control systems
Dynamical Systems
Dynamical Systems and Ergodic Theory
Fields (mathematics)
Homomorphisms
Lie groups
Mathematics
Mathematics and Statistics
Systems Theory
Vibration
34A05
Solutions
93B05
93C25
Controllability
Conjugation
34H05
Affine system
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Summary:The purpose of this paper is to present explicitly the solution curve for commutative affine control systems on Lie groups under the assumption that the automorphisms associated with the linear vector fields commutes. If we assume that the derivations associated with the linear vector fields of the system are inner, we obtain a simpler solution and we show some results of controllability. To finish, we work with conjugation by homomorphism of Lie groups between affine systems.
ISSN:1079-2724
1573-8698
DOI:10.1007/s10883-022-09591-4