Mathematical Programming

, Volume 168, Issue 1–2, pp 717–757 | Cite as

Optimal control of infinite dimensional bilinear systems: application to the heat and wave equations

  • M. Soledad Aronna
  • J. Frédéric Bonnans
  • Axel Kröner
Full Length Paper Series B


In this paper we consider second order optimality conditions for a bilinear optimal control problem governed by a strongly continuous semigroup operator, the control entering linearly in the cost function. We derive first and second order optimality conditions, taking advantage of the Goh transform. We then apply the results to the heat and wave equations.


Optimal control Partial differential equations Second-order optimality conditions Goh transform Semigroup theory Heat equation Wave equation Bilinear control systems 

Mathematics Subject Classification

49K20 35K05 35L05 90C48 


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Copyright information

© Springer-Verlag Berlin Heidelberg and Mathematical Optimization Society 2016

Authors and Affiliations

  1. 1.EMAp/FGVRio de JaneiroBrazil
  2. 2.Centre de Mathématiques Appliquées, Ecole Polytechnique, INRIA-SaclayUniversité Paris-SaclayPalaiseauFrance

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