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Time-optimal control of piecewise affine bistable gene-regulatory networks: preliminary results

Nicolas Augier 1, 2, 3 Agustín Gabriel yabo 1, 2, 3, 4 
1 BIOCORE - Biological control of artificial ecosystems
CRISAM - Inria Sophia Antipolis - Méditerranée , LOV - Laboratoire d'océanographie de Villefranche, INRAE - Institut National de Recherche pour l’Agriculture, l’Alimentation et l’Environnement
4 McTAO - Mathematics for Control, Transport and Applications
CRISAM - Inria Sophia Antipolis - Méditerranée
Abstract : In this preliminary work we give a geometric characterization of the time-optimal trajectories for a piecewise affine bistable switch. Such hybrid models play a major role in systems biology, as they can expressively account for the behaviors of simple gene-regulatory networks. A key example of these biological circuits is the genetic toggle switch, for which the optimality of a state switch has not been studied to the present day. The main tool of this work is an adaptation of the Hybrid Pontryagin's Maximum Principle to our setting, which allows to prove that the optimal control strategy is indeed a simple bang-bang feedback control law. In opposition to previous works, we show that a time-optimal transition between states should pass by an undifferentiated state, well known in cell biology for playing a major role in fate differentiation of cells. We conclude by showing numerical simulations of optimal trajectories illustrating the structure of the bang-bang optimal control for different scenarios.
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https://hal.inria.fr/hal-03099681
Contributor : Jean-Luc Gouzé Connect in order to contact the contributor
Submitted on : Saturday, January 9, 2021 - 9:42:11 AM
Last modification on : Saturday, June 25, 2022 - 11:49:02 PM

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Nicolas Augier, Agustín Gabriel yabo. Time-optimal control of piecewise affine bistable gene-regulatory networks: preliminary results. ADHS 2021 - 7th IFAC Conference on Analysis and Design of Hybrid Systems, IFAC, Jul 2021, Brussels, Belgium. ⟨10.1016/j.ifacol.2021.08.499⟩. ⟨hal-03099681v3⟩

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