Minimal time problem for a fed-batch bioreactor with a non admissible singular arc

International audienceIn this paper, we consider an optimal control problem for a system describing a fed-batch bioreactor with one species and one substrate. Our aim is to find an optimal feedback control in order to steer the system to a given target in minimal time. The growth function is of Haldane type implying the existence of a singular arc. Unlike many studies on the minimal time problem governed by an affine system w.r.t. the control with one input, we assume that the singular arc is non-necessary controllable. This brings interesting issues in terms of optimal synthesis. Thanks to the Pontryagin Maximum Principle, we provide the optimal synthesis of the problem, It turns out that singular extremal trajectories are no longer optimal on a subset of the singular arc

Analysis of an optimal control problem connected to bioprocesses involving a saturated singular arc

International audienceThis paper is devoted to the study of an optimal control problem under the presence of a saturation point on the singular locus. We consider the minimal time problem for a system describing a fed-batch reactor with one species and one substrate. Our aim is to find an optimal feedback control that steers the system to a given target in minimal time. The growth function is of Haldane type implying the existence of a singular arc. Unlike other studies on the minimal time problem governed by affine systems w.r.t. the control, we assume that the singular arc is non-necessary controllable everywhere. This brings interesting issues in terms of optimal synthesis. Thanks Pontryagin's Principle and numerical simulations, we provide an optimal synthesis of the problem

Locally prox-regular sets and variational inequalities

Les propriétés des ensembles localement prox-réguliers ont été étudiées par R.A. Poliquin, R.T. Rockafellar et L. Thibault. Le concept de fonction ''primal lower nice'' a été introduit en dimension finie par R.A. Poliquin et étendu au cadre Hilbertien par A.B. Levy, R.A. Poliquin et L. Thibault. Dans cette thèse, la première partie est consacrée à une étude des outils et des objets géométriques de l'Analyse non lisse tels que les fonctions primal lower nice et les ensembles localement prox-réguliers. On donnera une définition quantifiée de la prox-régularité locale. La deuxième partie établit des résultats d'existence et d'unicité de solutions d'inéquations variationnelles se présentant sous forme d'inclusions différentielles associées au cône normal d'un ensemble localement prox-régulier.The properties of locally prox-regular sets have been studied by R.A. Poliquin, R.T. Rockafellar and L. Thibault. R.A. Poliquin also introduced the concept of ``primal lower nice function. This dissertation is devoted, on one hand to the study of primal lower nice functions and locally prox-regular sets and, on the other hand, to show existence and uniqueness of solutions of differential variational inequalities involwing such sets. Concerning the first part, we introduce a quantified viewpoint of local-prox-regularity and establish a series of characterizations for set satisfying this property. In the second part, we study differential variational inequalities with locally prox-regular sets and we show the relevance of our quantified viewpoint to prove existence results of solutions

Lyapunov functions for evolution variational inequalities with locally prox-regular sets

This paper is devoted on the one hand to the study of specific properties of an evolution variational inequality, holding in the Hilbert setting. We give on the other hand a general criterion for Lyapunov pairs of this dynamical system and some results on the asymptotic behaviour of the solution

Ensembles localement prox-réguliers et inéquations variationnelles

Les propriétés des ensembles localement prox-réguliers ont été étudiées par R.A. Poliquin, R.T. Rockafellar et L. Thibault. Le concept de fonction ''primal lower nice'' a été introduit en dimension finie par R.A. Poliquin et étendu au cadre Hilbertien par A.B. Levy, R.A. Poliquin et L. Thibault. Dans cette thèse, la première partie est consacrée à une étude des outils et des objets géométriques de l'Analyse non lisse tels que les fonctions primal lower nice et les ensembles localement prox-réguliers. On donnera une définition quantifiée de la prox-régularité locale. La deuxième partie établit des résultats d'existence et d'unicité de solutions d'inéquations variationnelles se présentant sous forme d'inclusions différentielles associées au cône normal d'un ensemble localement prox-régulier.The properties of locally prox-regular sets have been studied by R.A. Poliquin, R.T. Rockafellar and L. Thibault. R.A. Poliquin also introduced the concept of primal lower nice function. This dissertation is devoted, on one hand to the study of primal lower nice functions and locally prox-regular sets and, on the other hand, to show existence and uniqueness of solutions of differential variational inequalities involwing such sets. Concerning the first part, we introduce a quantified viewpoint of local-prox-regularity and establish a series of characterizations for set satisfying this property. In the second part, we study differential variational inequalities with locally prox-regular sets and we show the relevance of our quantified viewpoint to prove existence results of solutions.MONTPELLIER-BU Sciences (341722106) / SudocSudocFranceF

Fed-batch bioreactor with mortality rate

International audienceWe address the problem of finding an optimal feedback control for feeding a fed-batchbioreactor with one species and one substrate, from a given initial condition to a given targetvalue in a minimal amount of time. Mortality rate for the biomass and nutrient recycling are taken into account in this work. The optimal synthesis (optimal feeding strategy) has been obtained by Moreno in 1999 when both mortality and recycling are considered negligible, in the case of Monod and Haldane growth function. Our objective is to study the effect of mortalityand recycling on the optimal synthesis. We provide an optimal synthesis of the problem usingPontryagin maximum principle, which extends the result of Moreno in the impulsive frameworkwith mortality and recycling effect

Use of the WHO Access, Watch, and Reserve classification to define patterns of hospital antibiotic use (AWaRe) : an analysis of paediatric survey data from 56 countries

Background Improving the quality of hospital antibiotic use is a major goal of WHO's global action plan to combat antimicrobial resistance. The WHO Essential Medicines List Access, Watch, and Reserve (AWaRe) classification could facilitate simple stewardship interventions that are widely applicable globally. We aimed to present data on patterns of paediatric AWaRe antibiotic use that could be used for local and national stewardship interventions. Methods 1-day point prevalence survey antibiotic prescription data were combined from two independent global networks: the Global Antimicrobial Resistance, Prescribing, and Efficacy in Neonates and Children and the Global Point Prevalence Survey on Antimicrobial Consumption and Resistance networks. We included hospital inpatients aged younger than 19 years receiving at least one antibiotic on the day of the survey. The WHO AWaRe classification was used to describe overall antibiotic use as assessed by the variation between use of Access, Watch, and Reserve antibiotics, for neonates and children and for the commonest clinical indications. Findings Of the 23 572 patients included from 56 countries, 18305 were children (77.7%) and 5267 were neonates (22.3%). Access antibiotic use in children ranged from 7.8% (China) to 61.2% (Slovenia) of all antibiotic prescriptions. The use of Watch antibiotics in children was highest in Iran (77.3%) and lowest in Finland (23.0%). In neonates, Access antibiotic use was highest in Singapore (100.0%) and lowest in China (24.2%). Reserve antibiotic use was low in all countries. Major differences in clinical syndrome-specific patterns of AWaRe antibiotic use in lower respiratory tract infection and neonatal sepsis were observed between WHO regions and countries. Interpretation There is substantial global variation in the proportion of AWaRe antibiotics used in hospitalised neonates and children. The AWaRe classification could potentially be used as a simple traffic light metric of appropriate antibiotic use. Future efforts should focus on developing and evaluating paediatric antibiotic stewardship programmes on the basis of the AWaRe index. Copyright (C) 2019 The Author(s). Published by Elsevier Ltd