A note on geometric algebras and control problems with SO(3)-symmetries
| Authors | |
|---|---|
| Year of publication | 2024 |
| Type | Article in Periodical |
| Magazine / Source | Mathematical Methods in the Applied Sciences |
| MU Faculty or unit | |
| Citation | HRDINA, Jaroslav, Aleš NÁVRAT, Petr VAŠÍK and Lenka ZALABOVÁ. A note on geometric algebras and control problems with SO(3)-symmetries. Mathematical Methods in the Applied Sciences. Wiley, 2024, vol. 47, No 3, p. 1257-1273. ISSN 0170-4214. Available from: https://dx.doi.org/10.1002/mma.8662. |
| 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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