Journal of Optimization Theory and Applications

, Volume 82, Issue 3, pp 503–517 | Cite as

Optimal feedback control for a semilinear evolution equation

  • M. I. Kamenskii
  • P. Nistri
  • V. V. Obukhovskii
  • P. Zecca
Contributed Papers

Abstract

In this paper, we consider a minimization problem of a cost functional associated to a nonlinear evolution feedback control system with a given boundary condition which includes the periodic one as a particular case. Specifically, by using an existence result for a system of inclusions involving noncompact operators (see Ref. 1), we first prove that the solution set of our problem is nonempty. Then, from the topological properties of this set, we derive the existence of a solution of the minimization problem under consideration.

Key Words

Evolution problems in Banach spaces optimal feedback controls measure of noncompactness topological degree 
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Copyright information

© Plenum Publishing Corporation 1994

Authors and Affiliations

  • M. I. Kamenskii
    • 1
  • P. Nistri
    • 2
  • V. V. Obukhovskii
    • 3
  • P. Zecca
    • 2
  1. 1.Department of MathematicsVoronezh State UniversityVoronezhRussia
  2. 2.Dipartimento di Sistemi e InformaticaUniversità di FirenzeFirenzeItaly
  3. 3.Department of Physics and MathematicsVoronezh State Pedagogical UniversityVoronezhRussia

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