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

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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.

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  • 19 May 2018

    We make corrections to the paper “Optimal Control of Infinite Dimensional Bilinear Systems: Application to the Heat and Wave Equations”, by M.S. Aronna, J.F. Bonnans, and A. Kröner, published in Mathematical Programming 168-1, (2018), pp. 717–757.


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Corresponding author

Correspondence to J. Frédéric Bonnans.

Additional information

Dedicated to Terry Rockafellar on the occasion of his 80th birthday.

The second and third author were supported by the project “Optimal control of partial differential equations using parameterizing manifolds, model reduction, and dynamic programming” funded by the Foundation Hadamard/Gaspard Monge Program for Optimization and Operations Research (PGMO).

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Aronna, M.S., Bonnans, J.F. & Kröner, A. Optimal control of infinite dimensional bilinear systems: application to the heat and wave equations. Math. Program. 168, 717–757 (2018). https://doi.org/10.1007/s10107-016-1093-4

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  • 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