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

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A Correction to this article was published on 19 May 2018

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Abstract

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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Correspondence to J. Frédéric Bonnans.

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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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  • DOI: https://doi.org/10.1007/s10107-016-1093-4

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