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Note on geometric algebras and control problems with SO(3)-symmetries
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  • Jaroslav Hrdina,
  • Aleš Návrat,
  • Petr Vašík,
  • Lenka Zalabova
Jaroslav Hrdina
Vysoke uceni technicke v Brne Fakulta strojniho inzenyrstvi

Corresponding Author:hrdina@fme.vutbr.cz

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Aleš Návrat
Vysoke uceni technicke v Brne Fakulta strojniho inzenyrstvi
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Petr Vašík
Vysoke uceni technicke v Brne
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Lenka Zalabova
Masaryk University
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Abstract

We study the role of symmetries in control systems by means of geometric algebra approach. We discuss two specific control problems on Carnot group of step 2 invariant with respect to the action of$SO(3). We understand geodesics as curves in suitable geometric algebras which allows us to asses an efficient algorithm for local control.

Peer review status:Published

22 Nov 2021Submitted to Mathematical Methods in the Applied Sciences
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23 Nov 2021Submission Checks Completed
23 Nov 2021Assigned to Editor
08 Dec 2021Reviewer(s) Assigned
25 May 2022Review(s) Completed, Editorial Evaluation Pending
03 Jun 2022Editorial Decision: Revise Minor
08 Jul 20221st Revision Received
09 Jul 2022Submission Checks Completed
09 Jul 2022Assigned to Editor
11 Jul 2022Reviewer(s) Assigned
08 Aug 2022Review(s) Completed, Editorial Evaluation Pending
09 Aug 2022Editorial Decision: Accept
30 Aug 2022Published in Mathematical Methods in the Applied Sciences. 10.1002/mma.8662