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Toward Geometric Time Minimal Control without Legendre Condition and with Multiple Singular Extremals for Chemical Networks. An Extended Version

Abstract : This article deals with the problem of maximizing the production of a species for a chemical network by controlling the temperature. Under the socalled mass kinetics assumption the system can be modeled as a single-input control system using the Feinberg-Horn-Jackson graph associated to the reactions network. Thanks to Pontryagin's Maximum Principle, the candidates as minimizers can be found among extremal curves, solutions of a (non smooth) Hamiltonian dynamics and the problem can be stated as a time minimal control problem with a terminal target of codimension one. Using geometric control and singularity theory the time minimal syntheses (closed loop optimal control) can be classified near the terminal manifold under generic conditions. In this article, we focus to the case where the generalized Legendre-Clebsch condition is not satisfied, which paves the road to complicated syntheses with several singular arcs. In particular, it is related to the situation for a weakly reversible network like the McKeithan scheme.
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https://hal.inria.fr/hal-03327127
Contributor : Jérémy Rouot Connect in order to contact the contributor
Submitted on : Thursday, August 26, 2021 - 7:46:36 PM
Last modification on : Saturday, June 25, 2022 - 11:51:55 PM
Long-term archiving on: : Saturday, November 27, 2021 - 6:47:55 PM

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  • HAL Id : hal-03327127, version 1

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Bernard Bonnard, Jérémy Rouot. Toward Geometric Time Minimal Control without Legendre Condition and with Multiple Singular Extremals for Chemical Networks. An Extended Version. [Research Report] INRIA Sophia Antipolis - Méditerranée; LMBA. 2021. ⟨hal-03327127⟩

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