Stabilization of higher order Schrödinger equations on a finite interval: part II

buir.contributor.authorÖzsarı, Türker
buir.contributor.orcidÖzsarı, Türker|0000-0003-4240-5252
dc.citation.epage62en_US
dc.citation.spage1en_US
dc.contributor.authorÖzsarı, Türker
dc.contributor.authorYılmaz, K. C.
dc.date.accessioned2022-03-01T13:16:14Z
dc.date.available2022-03-01T13:16:14Z
dc.date.issued2021-07
dc.departmentDepartment of Mathematicsen_US
dc.description.abstractBackstepping based controller and observer models were designed for higher order linear and nonlinear Schrödinger equations on a finite interval in [3] where the controller was assumed to be acting from the left endpoint of the medium. In this companion paper, we further the analysis by considering boundary controller(s) acting at the right endpoint of the domain. It turns out that the problem is more challenging in this scenario as the associated boundary value problem for the backstepping kernel becomes overdetermined and lacks a smooth solution. The latter is essential to switch back and forth between the original plant and the so called target system. To overcome this difficulty we rely on the strategy of using an imperfect kernel, namely one of the boundary conditions in kernel PDE model is disregarded. The drawback is that one loses rapid stabilization in comparison with the left endpoint controllability. Nevertheless, the exponential decay of the L2-norm with a certain rate still holds. The observer design is associated with new challenges from the point of view of wellposedness and one has to prove smoothing properties for an associated initial boundary value problem with inhomogeneous boundary data. This problem is solved by using Laplace transform in time. However, the Bromwich integral that inverts the transformed solution is associated with certain analyticity issues which are treated through a subtle analysis. Numerical algorithms and simulations verifying the theoretical results are given.en_US
dc.identifier.doi10.3934/eect.2021037en_US
dc.identifier.eissn2163-2480
dc.identifier.issn2163-2472
dc.identifier.urihttp://hdl.handle.net/11693/77658
dc.language.isoEnglishen_US
dc.publisherAIMS Pressen_US
dc.relation.isversionofhttps://doi.org/10.3934/eect.2021037en_US
dc.source.titleEvolution Equations and Control Theoryen_US
dc.subjectHigher order Schrödinger equationen_US
dc.subjectBacksteppingen_US
dc.subjectStabilizationen_US
dc.subjectObserveren_US
dc.subjectBoundary controlleren_US
dc.subjectExponential stabilityen_US
dc.titleStabilization of higher order Schrödinger equations on a finite interval: part IIen_US
dc.typeArticleen_US

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