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Conference Papers Year : 2021

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

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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Dates and versions

hal-03099681 , version 1 (06-01-2021)
hal-03099681 , version 2 (06-01-2021)
hal-03099681 , version 3 (09-01-2021)
hal-03099681 , version 4 (09-01-2023)

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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-03099681v4⟩
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