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.
Related projects:	Symetrie a invariance v analýze, geometrickém modelování a teorii optimálního řízení