Constructing Transverse Coordinates for Orbital Stabilization of Periodic Trajectories

Maksim Surov, Sergei Gusev, Leonid Freidovich

Research output: Chapter in Book/Report/Conference proceedingConference contributionResearchpeer-review


An approach for introduction of transverse coordinates in a vicinity of a periodic trajectory is presented. The approach allows finding by numerical integration periodic normalized mutually-orthogonal vector-functions that form a continuously differentiable basis on moving Poincaré sections for a given periodic solution of a nonlinear dynamical system.The found moving frame is used to define new local (transverse) coordinates for an associated affine nonlinear control system in a neighborhood of the trajectory, and to proceed with orbital stability analysis and/or synthesis of a stabilizing feedback control law.As a demonstrating example of the approach, the problem of orbital stabilization of a trajectory of a multibody car system is considered. The results of computer simulations of the system are presented.

Original languageEnglish
Title of host publication2020 American Control Conference, ACC 2020
PublisherInstitute of Electrical and Electronics Engineers Inc.
Number of pages6
ISBN (Electronic)9781538682661
StatePublished - Jul 2020
Event2020 American Control Conference, ACC 2020 - Denver, United States
Duration: 1 Jul 20203 Jul 2020

Publication series

NameProceedings of the American Control Conference
ISSN (Print)0743-1619


Conference2020 American Control Conference, ACC 2020
CountryUnited States

Scopus subject areas

  • Electrical and Electronic Engineering

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