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Robust orbital stabilization: A Floquet theory-based approach
Department of Engineering Cybernetics, NTNU, Trondheim, Norway.
Department of Engineering Cybernetics, NTNU, Trondheim, Norway; Department of Information Technologies and AI, Sirius University of Science and Technology, Sochi, Russian Federation.
Umeå University, Faculty of Science and Technology, Department of Applied Physics and Electronics. Department of Information Technologies and AI, Sirius University of Science and Technology, Sochi, Russian Federation.ORCID iD: 0000-0003-0730-9441
Department of Information Technologies and AI, Sirius University of Science and Technology, Sochi, Russian Federation.
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2021 (English)In: International Journal of Robust and Nonlinear Control, ISSN 1049-8923, E-ISSN 1099-1239, Vol. 31, no 16, p. 8075-8108Article in journal (Refereed) Published
Abstract [en]

The design of robust orbitally stabilizing feedback is considered. From a known orbitally stabilizing controller for a nominal, disturbance-free system, a robustifying feedback extension is designed utilizing the sliding-mode control (SMC) methodology. The main contribution of the article is to provide a constructive procedure for designing the time-invariant switching function used in the SMC synthesis. More specifically, its zero-level set (the sliding manifold) is designed using a real Floquet–Lyapunov transformation to locally correspond to an invariant subspace of the Monodromy matrix of a transverse linearization. This ensures asymptotic stability of the periodic orbit when the system is confined to the sliding manifold, despite any system uncertainties and external disturbances satisfying a matching condition. The challenging task of oscillation control of the underactuated cart–pendulum system subject to both matched- and unmatched disturbances/uncertainties demonstrates the efficacy of the proposed scheme.

Place, publisher, year, edition, pages
John Wiley & Sons, 2021. Vol. 31, no 16, p. 8075-8108
Keywords [en]
orbital stabilization, robust nonlinear control, sliding mode control, underactuated mechanical systems
National Category
Control Engineering
Identifiers
URN: urn:nbn:se:umu:diva-187289DOI: 10.1002/rnc.5738ISI: 000693307400001Scopus ID: 2-s2.0-85113977209OAI: oai:DiVA.org:umu-187289DiVA, id: diva2:1591893
Available from: 2021-09-07 Created: 2021-09-07 Last updated: 2022-01-11Bibliographically approved

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Freidovich, Leonid B.

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