This work was partially supported by CNPq/Universal grant no. 476024/2012-9 and the second author was supported by Fundação Araucária grant no. 20134003.
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.
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Über diesen Artikel
Hermes-Sussmann and ad-rank Conditions for Local Controllability
Osvaldo G. do Rocio Alexandre J. Santana Marcos A. Verdi