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An extended controllability problem with minimum energy

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Abstract

The aim of this paper is to consider an output controllability problem. It consists in driving the state of a distributed parabolic system toward a state between two prescribed functions on a boundary subregion of the system evolution domain with minimum energy control. Two necessary conditions are given. The first is formulated in terms of the subdifferential associated with a minimized functional. The second is formulated as a system of equations for arguments of the Lagrange systems. Numerical illustrations show the efficiency of the second approach and lead to open questions.

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Authors and Affiliations

  1. MACS Group - AFACS UFR, Department of Mathematics and Computer Sciences, Moulay Ismail University, Faculty of Sciences, Meknes, Morocco

    E. Zerrik, F. Ghafrani & M. Raïssouli

Authors
  1. E. Zerrik
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  2. F. Ghafrani
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  3. M. Raïssouli
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Corresponding author

Correspondence to E. Zerrik.

Additional information

Translated from Sovremennaya Matematika i Ee Prilozheniya (Contemporary Mathematics and Its Applications), Vol. 61, Optimal Control, 2008.

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Zerrik, E., Ghafrani, F. & Raïssouli, M. An extended controllability problem with minimum energy. J Math Sci 161, 344–354 (2009). https://doi.org/10.1007/s10958-009-9558-0

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  • DOI: https://doi.org/10.1007/s10958-009-9558-0

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