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Control Systems on Three-Dimensional Lie Groups: Equivalence and Controllability

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Abstract

We consider left-invariant control affine systems, evolving on three-dimensional matrix Lie groups. Equivalence and controllability are investigated. All full-rank systems are classified, under detached feedback equivalence. A representative is identified for each equivalence class. The controllability nature of these representatives is determined.

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Authors and Affiliations

  1. Department of Mathematics (Pure and Applied), Rhodes University, PO Box 94, 6140, Grahamstown, South Africa

    Rory Biggs & Claudiu C. Remsing

Authors
  1. Rory Biggs
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  2. Claudiu C. Remsing
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Correspondence to Claudiu C. Remsing.

Appendix

Appendix

Table 2 Characterization of controllability for full-rank systems
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Table 3 Classification of controllable systems on (completely) solvable groups
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Table 4 Classification of controllable systems on solvable groups (cont.)
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Table 5 Classification of controllable systems on semisimple groups
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Biggs, R., Remsing, C.C. Control Systems on Three-Dimensional Lie Groups: Equivalence and Controllability. J Dyn Control Syst 20, 307–339 (2014). https://doi.org/10.1007/s10883-014-9212-0

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  • DOI: https://doi.org/10.1007/s10883-014-9212-0

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