Note on geometric algebras and control problems with SO(3)-symmetries

Jaroslav Hrdina; Ales Navrat; Petr Vasik; Lenka Zalabova

Note on geometric algebras and control problems with SO(3)-symmetries

Differential Geometry 2022-09-02 v2 Dynamical Systems Optimization and Control

Authors: Jaroslav Hrdina , Ales Navrat , Petr Vasik , Lenka Zalabova

Abstract

We study the role of symmetries in control systems through the geometric algebra approach. We discuss two specific control problems on Carnot groups of step $2$ invariant with respect to the action of $SO(3)$ . We understand the geodesics as the curves in suitable geometric algebras which allows us to assess a new algorithm for the local control.

Keywords

algebraic geometry geodesics and riemannian geometry curves

Cite

@article{arxiv.2111.11088,
  title  = {Note on geometric algebras and control problems with SO(3)-symmetries},
  author = {Jaroslav Hrdina and Ales Navrat and Petr Vasik and Lenka Zalabova},
  journal= {arXiv preprint arXiv:2111.11088},
  year   = {2022}
}

Comments

Final version, few mistakes corrected

Note on geometric algebras and control problems with SO(3)-symmetries

Abstract

Keywords

Cite

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