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

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Authors

HRDINA Jaroslav NÁVRAT Aleš VAŠÍK Petr ZALABOVÁ Lenka

Year of publication 2024
Type Article in Periodical
Magazine / Source Mathematical Methods in the Applied Sciences
MU Faculty or unit

Faculty of Science

Citation
Web https://doi.org/10.1002/mma.8662
Doi http://dx.doi.org/10.1002/mma.8662
Keywords Carnot groups; geometric algebras; local control and optimality; sub-Riemannian geodesics; symmetries
Description 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.
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