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Hermes-Sussmann and ad-rank Conditions for Local Controllability

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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.

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Acknowledgments

We are very grateful for the suggestions of Prof. Luiz A.B. San Martin at the beginning of this work. We also thank the anonymous referees for their careful reading of our manuscript and their comments and suggestions.

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Authors and Affiliations

  1. Mathematics Department, State University of Maringa (UEM), 87020-900, Maringa, Brazil

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

Authors
  1. Osvaldo G. do Rocio
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  2. Alexandre J. Santana
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  3. Marcos A. Verdi
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Corresponding author

Correspondence to Alexandre J. Santana.

Additional information

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.

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do Rocio, O.G., Santana, A.J. & Verdi, M.A. Hermes-Sussmann and ad-rank Conditions for Local Controllability. J Dyn Control Syst 23, 535–545 (2017). https://doi.org/10.1007/s10883-016-9340-9

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  • DOI: https://doi.org/10.1007/s10883-016-9340-9

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