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Optimal Control of a Class of Size-Structured Systems

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Large-Scale Scientific Computing (LSSC 2007)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 4818))

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Abstract

Optimality conditions of Pontryagin’s type are obtained for an optimal control problem for a size-structured system described by a first order PDE where the differential operator depends on a control and on an aggregated state variable. Typically in this sort of problems the state function is not differentiable, even discontinuous, which creates difficulties for the variational analysis. Using the method of characteristics (which are control and state dependent for the considered system) the problem is reformulated as an optimization problem for a heterogeneous control system, investigated earlier by the second author. Based on this transformation, the optimality conditions are obtained and a stylized meaningful example is given where the optimality conditions allow to obtain an explicit differential equation for the optimal control.

The first author was supported for this research by the grant CNCSIS 1416/2005, and the second — by the Austrian Science Foundation (FWF) under grant P18161.

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Author information

Authors and Affiliations

  1. Faculty of Mathematics, “Al. I. Cuza” University, Romania

    Oana Carmen Tarniceriu

  2. Institute Mathematical Methods in Economics, Vienna University of Technology, Wiedner Hauptstr. 8–10/115, A-1040, Vienna, Austria

    Vladimir M. Veliov

  3. Institute of Mathematics and Informatics, Bulgarian Academy of Sciences, Bulgaria

    Vladimir M. Veliov

Authors
  1. Oana Carmen Tarniceriu
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  2. Vladimir M. Veliov
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Editor information

Editors and Affiliations

  1. Institute for Parallel Processing, Bulgarian Academy of Sciences, Acad. G. Bonchev, Bl. 25A, 1113, Sofia, Bulgaria

    Ivan Lirkov

  2. Institute for Parallel Processing, Bulgarian Academy of Sciences, Acad. G. Bonchev Str. Bl. 25-A, 1113, Sofia, Bulgaria

    Svetozar Margenov

  3. Department of Informatics and Mathematical Modelling, Technical University of Denmark, Richard Petersen Plads, Building 321, DK-2800, Kongens Lyngby, Denmark

    Jerzy Waśniewski

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Tarniceriu, O.C., Veliov, V.M. (2008). Optimal Control of a Class of Size-Structured Systems. In: Lirkov, I., Margenov, S., Waśniewski, J. (eds) Large-Scale Scientific Computing. LSSC 2007. Lecture Notes in Computer Science, vol 4818. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-78827-0_41

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  • DOI: https://doi.org/10.1007/978-3-540-78827-0_41

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-78825-6

  • Online ISBN: 978-3-540-78827-0

  • eBook Packages: Computer ScienceComputer Science (R0)

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