Optimal Control of an Age-Structured System with State Constraints

Abstract : The aim of this work is to study an optimal control problem with state constraints where the state is given by an age-structured, abstract parabolic differential equation. We prove the existence and uniqueness of solution for the state equation and provide first and second parabolic estimates. We analyze the differentiability of the cost function and, based on the general theory of Lagrange multipliers, we give a first order optimality condition. We also define and analyze the regularity of the costate. Finally, we present a pregnancy model, where two coupled age-structured equations are involved, and we apply the obtained results to this case.
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Submitted on : Tuesday, June 25, 2019 - 1:15:35 AM
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Joseph Frédéric Bonnans, Justina Gianatti. Optimal Control of an Age-Structured System with State Constraints. 2019. ⟨hal-02164310⟩

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