Stability and optimal control

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dc.authorid0000-0002-3972-2591en_US
dc.contributor.authorRemsing, C. C.
dc.date.accessioned2024-07-12T20:49:58Z
dc.date.available2024-07-12T20:49:58Z
dc.date.issued2009en_US
dc.departmentFakülteler, İnsan ve Toplum Bilimleri Fakültesi, Matematik Bölümüen_US
dc.description.abstractWe consider the problem of minimizing a quadratic cost functional J = 1 2 R T 0 ¡ c1u 2 1 + · · · + c`u 2 ` ¢ dt over the trajectories of a left-invariant control system ? evolving on a matrix Lie group G, which is affine in controls. The final time T > 0 is fixed and there are no restrictions on the values of the control variables. Each such invariant optimal control problem defines the appropriate Hamiltonian H on the dual g ? of the Lie algebra of G through the Pontryagin’s Maximum Principle. The integral curves of the corresponding Hamiltonian vector field H~ (with respect to the minus Lie-Poisson structure on g ? ) are called extremal curves. In this paper we are concerned with regular extremal curves. When the Lie algebra g admits a non-degenerate invariant bilinear form h·, ·i : g × g ? R, the Hamilton equations take a more familiar form. This is always possible if g is semisimple. Lyapunov stability of Hamiltonian equilibria is investigated by using the energy-Casimir method. Explicit computations are done in the special case of the rotation group SO (3).en_US
dc.identifier.citationRemsing, C. C. (2009). Stability and optimal control. Maltepe Üniversitesi. s. 126.en_US
dc.identifier.endpage127en_US
dc.identifier.isbn9.78605E+12
dc.identifier.startpage126en_US
dc.identifier.urihttps://www.maltepe.edu.tr/Content/Media/CkEditor/03012019014112056-AbstractBookICMS2009Istanbul.pdf#page=331
dc.identifier.urihttps://hdl.handle.net/20.500.12415/2264
dc.institutionauthorRemsing, C. C.
dc.language.isoenen_US
dc.publisherMaltepe Üniversitesien_US
dc.relation.ispartofInternational Conference of Mathematical Sciencesen_US
dc.relation.publicationcategoryUluslararası Konferans Öğesi - Başka Kurum Yazarıen_US
dc.rightsCC0 1.0 Universal*
dc.rightsinfo:eu-repo/semantics/openAccessen_US
dc.rights.urihttp://creativecommons.org/publicdomain/zero/1.0/*
dc.snmzKY07591
dc.titleStability and optimal controlen_US
dc.typeConference Object
dspace.entity.typePublication

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