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Article Dans Une Revue Mathematical Control and Related Fields Année : 2020

Optimal periodic control for scalar dynamics under integral constraint on the input

Résumé

This paper studies a periodic optimal control problem governed by a one-dimensional system, linear with respect to the control u, under an integral constraint on u. We give conditions for which the value of the cost function at steady state with a constant control \bar u can be improved by considering periodic control u with average value equal to \bar u. This leads to the so-called "over-yielding" met in several applications. With the use of the Pontryagin Maximum Principle, we provide the optimal synthesis of periodic strategies under the integral constraint. The results are illustrated on a single population model in order to study the effect of periodic inputs on the utility of the stock of resource.
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Dates et versions

hal-02057590 , version 1 (05-03-2019)
hal-02057590 , version 2 (09-09-2019)

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Citer

Térence Bayen, Alain Rapaport, Fatima Zahra Tani. Optimal periodic control for scalar dynamics under integral constraint on the input. Mathematical Control and Related Fields, 2020, 10 (3), pp.547-571. ⟨10.3934/mcrf.2020010⟩. ⟨hal-02057590v2⟩
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