Scopus İndeksli Yayınlar Koleksiyonu / Scopus Indexed Publications Collection

Permanent URI for this collectionhttps://hdl.handle.net/11147/7148

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Author: search.filters.author.Kalantarov, Varga K.

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  • Article
    Finite-Dimensional Backstepping Controller Design
    (Ieee-inst Electrical Electronics Engineers inc, 2025) Kalantarov, Varga K.; Ozsari, Turker; Yilmaz, Kemal Cem
    In this article, we introduce a finite-dimensional version of backstepping controller design for stabilizing solutions of partial differential equations (PDEs) from boundary. Our controller uses only a finite number of Fourier modes of the state of solution, as opposed to the classical backstepping controller which uses all (infinitely many) modes. We apply our method to the reaction-diffusion equation, which serves only as a canonical example but the method is applicable also to other PDEs whose solutions can be decomposed into a slow finite-dimensional part and a fast tail, where the former dominates the evolution in large time. One of the main goals is to estimate the sufficient number of modes needed to stabilize the plant at a prescribed rate. In addition, we find the minimal number of modes that guarantee the stabilization at a certain (unprescribed) decay rate. Theoretical findings are supported with numerical solutions.
  • Article
    Citation - WoS: 14
    Citation - Scopus: 15
    Qualitative Properties of Solutions for Nonlinear Schrödinger Equations With Nonlinear Boundary Conditions on the Half-Line
    (American Institute of Physics, 2016) Kalantarov, Varga K.; Özsarı, Türker
    In this paper, we study the interaction between a nonlinear focusing Robin type boundary source, a nonlinear defocusing interior source, and a weak damping term for nonlinear Schrödinger equations posed on the infinite half-line. We construct solutions with negative initial energy satisfying a certain set of conditions which blow-up in finite time in the H1-sense. We obtain a sufficient condition relating the powers of nonlinearities present in the model which allows construction of blow-up solutions. In addition to the blow-up property, we also discuss the stabilization property and the critical exponent for this model.