A time-delay equation: well-posedness to optimal control

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dc.authoridyildirim, kenan/0000-0002-4471-3964
dc.contributor.authorYildirim, Kenan
dc.contributor.authorAlkan, Sertan
dc.date.accessioned2024-09-18T21:00:41Z
dc.date.available2024-09-18T21:00:41Z
dc.date.issued2016
dc.departmentHatay Mustafa Kemal Üniversitesien_US
dc.description.abstractIn this paper, well-posedness, controllability and optimal control for a time-delay beam equation are studied. The equation of motion is modeled as a time-delayed distributed parameter system(DPS) and includes Heaviside functions and their spatial derivatives due to the finite size of piezoelectric patch actuators used to suppress the excessive vibrations based on displacement and moment conditions. The optimal control problem is defined with the performance index including a weighted quadratic functional of the displacement and velocity which is to be minimized at a given terminal time and a penalty term defined as the control voltage used in the control duration. Optimal control law is obtained by using Maximum principle and hence, the optimal control problem is transformed the into a boundary-, initial and terminal value problem. The explicit solution of the control problem is obtained by eigenfunction expansions of the state and adjoint variables. Numerical results are presented to show the effectiveness and applicability of the piezoelectric control.en_US
dc.identifier.doi10.1515/phys-2016-0026
dc.identifier.endpage220en_US
dc.identifier.issn2391-5471
dc.identifier.issue1en_US
dc.identifier.scopus2-s2.0-84979587966en_US
dc.identifier.scopusqualityQ2en_US
dc.identifier.startpage212en_US
dc.identifier.urihttps://doi.org/10.1515/phys-2016-0026
dc.identifier.urihttps://hdl.handle.net/20.500.12483/12820
dc.identifier.volume14en_US
dc.identifier.wosWOS:000385764000007en_US
dc.identifier.wosqualityQ3en_US
dc.indekslendigikaynakWeb of Scienceen_US
dc.indekslendigikaynakScopusen_US
dc.language.isoenen_US
dc.publisherDe Gruyter Open Ltden_US
dc.relation.ispartofOpen Physicsen_US
dc.relation.publicationcategoryMakale - Uluslararası Hakemli Dergi - Kurum Öğretim Elemanıen_US
dc.rightsinfo:eu-repo/semantics/openAccessen_US
dc.subjectWellposednessen_US
dc.subjectTime-delayen_US
dc.subjectVibrationen_US
dc.subjectControlen_US
dc.subjectMaximum Principleen_US
dc.titleA time-delay equation: well-posedness to optimal controlen_US
dc.typeArticleen_US

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