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