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Journal of Dynamical and Control Systems

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15-08-2016

Hermes-Sussmann and ad-rank Conditions for Local Controllability

Authors: Osvaldo G. do Rocio, Alexandre J. Santana, Marcos A. Verdi

Published in: Journal of Dynamical and Control Systems | Issue 3/2017

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Abstract

In this paper, we consider linear control systems on Lie groups and compare three different approaches to local controllability for these systems: Hermes-Sussmann conditions, Hermes condition, and ad-rank condition. We prove that the ad-rank condition can be deduced from the Hermes-Sussmann conditions. We also prove that the Hermes condition and the ad-rank condition are equivalent in case of systems with scalar control. As application, we provide a criterion for global controllability for restricted linear systems on the Heisenberg group.

previous article First Variation of the Hausdorff Measure of Non-horizontal Submanifolds in Sub-Riemannian Stratified Lie Groups

next article Sub-Finsler Structures from the Time-Optimal Control Viewpoint for some Nilpotent Distributions

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Title: Hermes-Sussmann and ad-rank Conditions for Local Controllability
Authors: Osvaldo G. do Rocio
Alexandre J. Santana
Marcos A. Verdi
Publication date: 15-08-2016
Publisher: Springer US
Published in: Journal of Dynamical and Control Systems / Issue 3/2017
Print ISSN: 1079-2724
Electronic ISSN: 1573-8698
DOI: https://doi.org/10.1007/s10883-016-9340-9

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