2019/11/14 by Christian Fredrik Sætre, Sætre, Christian Fredrik, Anton Shiriaev +1
Engineering · #Aerospace Engineering and Control Systems #Control and Dynamics of Mobile Robots #FOS: Electrical engineering #Spacecraft Dynamics and Control #Systems and Control (eess.SY) #electronic engineering #information engineering
paper · pdf · doi:10.48550/arxiv.1911.06232
openalex publication_date 2019/11/14 · openalex created_date 2022/07/26 · openalex updated_date 2026/07/28
This paper explores transverse coordinates for the purpose of orbitally\nstabilizing periodic motions of nonlinear, control-affine dynamical systems. It\nis shown that the dynamics of any (minimal or excessive) set of transverse\ncoordinates, which are defined in terms of a particular parameterization of the\nmotion and a strictly state-dependent projection operator recovering the\nparameterizing variable, admits a (transverse) linearization along the target\nmotion, with explicit expressions stated. Special focus is then placed on a\ngeneric excessive set of orthogonal coordinates, revealing a certain limitation\nof the "excessive" transverse linearization for the purpose of control design.\nTo overcome this limitation, a linear comparison system is introduced, and\nconditions are stated for when the asymptotic stability of its origin\ncorresponds to the asymptotic stability of the origin of linearized transverse\ndynamics. This allows for the construction of feedback controllers utilizing\nthis comparison system which, when implemented on the dynamical system, renders\nthe desired motion asymptotically stable in the orbital sense.\n