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

2021/11/22 by Hrdina, Jaroslav, Navrat, Ales, Vasik, Petr +1
#22E60 #53C17 #93C15 #Differential Geometry (math.DG) #Dynamical Systems (math.DS) #FOS: Mathematics #Optimization and Control (math.OC)

paper · doi:10.48550/arxiv.2111.11088

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.

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