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

Abstract : 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 U can be improved by considering periodic control u with average value equal to 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 problem of water quality in the chemostat model with periodic dilution rate, for various growth functions.
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Submitted on : Wednesday, February 28, 2018 - 8:48:15 PM
Last modification on : Tuesday, May 28, 2019 - 1:54:03 PM
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  • HAL Id : hal-01700128, version 4

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Térence Bayen, Alain Rapaport, Fatima-Zahra Tani. Optimal periodic control for scalar dynamics under integral constraint on the input . 2018. ⟨hal-01700128v4⟩

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