Optimal Control of a Class of Size-Structured Systems

  • Oana Carmen Tarniceriu
  • Vladimir M. Veliov
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4818)


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.


Optimal Control Problem Adjoint System Gradient Projection Method Population Context Continuous Dependence Result 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2008

Authors and Affiliations

  • Oana Carmen Tarniceriu
    • 1
  • Vladimir M. Veliov
    • 2
    • 3
  1. 1.Faculty of Mathematics“Al. I. Cuza” UniversityRomania
  2. 2.Institute Mathematical Methods in EconomicsVienna University of TechnologyViennaAustria
  3. 3.Institute of Mathematics and InformaticsBulgarian Academy of SciencesBulgaria

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