Térence Bayen

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This paper is devoted to the minimal time control problem for fed-batch bioreactors, in presence of an inhibitory product, which is released by the biomass proportionally to its growth. We first consider a growth rate with substrate saturation and product inhibition, and we prove that the optimal strategy is fill and wait (bang-bang). We then investigate(More)
We present a complete analytic parametrization of constant width bodies in dimension 3 based on the median surface: more precisely, we define a bijection between some space of functions and constant width bodies. We compute simple geometrical quantities like the volume and the surface area in terms of those functions. As a corollary we give a new algebraic(More)
We address the problem of finding an optimal feedback control for feeding a fed-batch bioreactor with one species and one substrate from a given initial condition to a given target value in a minimal amount of time. Recently, the optimal synthesis (optimal feeding strategy) has been obtained in systems in which the microorganisms involved are represented by(More)
Curves which can be rotated freely in an n-gon (that is, an regular polygon with n sides) so that they always remain in contact with every side of the n-gon are called rotors. Using optimal control theory, we prove that the rotor with minimal area consists of a finite union of arcs of circles. Moreover, the radii of these arcs are exactly the distances of(More)
The article is devoted to the analysis of two models describing the goal-oriented locomotion. We first consider a system proposed by Laumond et al. (see [3]) for which the control on the derivative of the curvature κ̇ along the trajectory is supposed bounded. Necessary conditions on optimal trajectories are given. We then investigate an extension of this(More)
We study the minimum time control problem of a series of two interconnected chemostats under the input constraint u2 ≤ u1, where ui are the respective dilution rates in the tanks. This constraint brings controllability issues in the study of the optimal strategies. We encounter this difficulty by splitting the state domain into two sub-domains, one with no(More)
We study a minimal time control problem under the presence of a saturation point on the singular locus. The system describes a fed-batch reactor with one species and one substrate. Our aim is to find an optimal feedback control steering the system to a given target in minimal time. The growth function is of Haldane type implying the existence of a singular(More)
In this work, we study the coupling of a culture of micro-algae limited by light and an anaerobic digester in a two-tank bioreactor. The model for the reactor combines a periodic day-night light for the culture of microalgae and a classical chemostat model for the digester. We first prove the existence and attraction of periodic solutions of this problem(More)