Optimal control theory and the efficiency of the swimming mechanism of the Copepod Zooplankton

International audienceIn this article, the model of swimming at low Reynolds number introduced by D. Takagi (2015) to analyze the displacement of an abundant variety of zooplankton is used as a testbed to analyze the motion of symmetric microswimmers in the framework of optimal control theory assuming that the motion occurs minimizing the energy dissipated by the fluid drag forces in relation with the concept of efficiency of a stroke. The maximum principle is used to compute periodic controls candidates as minimizing controls and is a decisive tool combined with appropriate numerical simulations using indirect optimal control schemes to determine the most efficient stroke compared with standard computations using Stokes theorem and curvature control. Also the concept of graded approximations in SR-geometry is used to evaluate strokes with small amplitudes providing a fixed displacement and minimizing the dissipated energy

The Purcell Three-link swimmer: some geometric and numerical aspects related to periodic optimal controls

International audienceThe maximum principle combined with numerical methods is a powerful tool to compute solutions for optimal control problems. This approach turns out to be extremely useful in applications, including solving problems which require establishing periodic trajectories for Hamiltonian systems, optimizing the production of photobioreactors over a one-day period, finding the best periodic controls for locomotion models (e.g. walking, flying and swimming). In this article we investigate some geometric and numerical aspects related to optimal control problems for the so-called Purcell Three-link swimmer [20], in which the cost to minimize represents the energy consumed by the swimmer. More precisely, employing the maximum principle and shooting methods we derive optimal trajectories and controls, which have particular periodic features. Moreover, invoking a linearization procedure of the control system along a reference extremal, we estimate the conjugate points, which play a crucial role for the second order optimality conditions. We also show how, making use of techniques imported by the sub-Riemannian geometry, the nilpotent approximation of the system provides a model which is integrable, obtaining explicit expressions in terms of elliptic functions. This approximation allows to compute optimal periodic controls for small deformations of the body, allowing the swimmer to move minimizing its energy. Numerical simulations are presented using Hampath and Bocop codes

Feedback Classification and Optimal Control with Applications to the Controlled Lotka-Volterra Model

Let M be a σ-compact C^∞ manifold of dimension n ≥ 2 and consider a single-input control system: ẋ(t) = X (x(t)) + u(t) Y (x(t)), where X , Y are C^∞ vector fields on M. We prove that there exist an open set of pairs (X , Y ) for the C^∞ –Whitney topology such that they admit singular abnormal rays so that the spectrum of the projective singular Hamiltonian dynamics is feedback invariant. It is applied to controlled Lotka–Volterra dynamics where such rays are related to shifted equilibria of the free dynamics

Geometric Optimal Control of the Generalized Lotka-Volterra Model with Applications Controlled Stability of Microbiota

International audienceIn this talk we present the Generalized Lotka–Volterra dynamics associated to themodel of C-difficile infection of the intestine microbiote and aiming to transfer the systemfrom an infected state to an healthy state. The control inputs are of two types : fecalinjection or bactericides which act as Dirac pulses and prebiotics or antibiotics which act ascontinuous controls. An uniform frame can be introduced using the tools from geometriccontrol to analyze the accessibility set as the orbit of a pseudo-semi group. Optimalcontrol can be considered in the frame of permanent control or sampled-data control. Thelater being adapted to the practical constraints of a finite set of medical interventions. Inboth case the optimal control problems can be analyzed using direct and indirect schemesaiming to reach an healthy state. Such methods are tested on toys models in dimension 2and 3 related to the construction of reduced dynamics. Even those simple situations leadto interesting questions of accessibility and integrability issues in relation with the studyof dynamical systems

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

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

Collectivités locales/prêteurs

Toute relation de crédit est par essence, génératrice de risques pour les deux partenaires : les collectivités locales et leurs prêteurs (parmi les plus emblématiques, Dexia Crédit Local et la Caisse des Dépôts et Consignations). Leurs communications financières font l’objet d’une comparaison, au travers d’une analyse textuelle. La sociologie du risque et la théorie des « pôles culturels » proposent une lecture de la communication de ces organisations et décryptent la mutation du système de financement des collectivités locales françaises actuellement à l’œuvre.Any credit relationship generates, by definition, risks for both partners : local governments and their lenders (among the most famous : Dexia Crédit Local and Caisse des Dépôts et Consignations). Their financial communications are the subject of a comparison, through a textual analysis. The sociology of risk and the “cultural theory” propose a reading of the communication of these organizations and shed light on the current changes in the financing system of the French local governments

Communication financière des collectivités locales françaises et crise internationale : des pratiques en mutation

La crise internationale a frappé les budgets des collectivités locales françaises et leur encours de dettes, notamment via les produits structurés. Il est alors légitime de s’interroger sur l’impact de cette crise sur leur communication financière. Cette recherche consiste en une analyse textuelle du contenu des rapports annuels ou financiers, par le logiciel Alceste. Une discussion des résultats au regard de la littérature sur les stratégies de communication fait apparaitre 2008, comme une année de bouleversements et dessine un cheminement allant de la « reconnaissance » au « changement ».The international crisis has affected budgets of French local governments and their debts, particularly through structured products. It’s well-founded to wonder about the impact of this crisis on their financial communication. This research is a textual analysis of the content of annual or financial reports by Alceste software. Discussing results based on a literature survey on communication strategies brings up 2008 as a year of confusion and highlights a shift from “recognition” to “change”

La communication financière des collectivités territoriales : nouveaux usages de l’Internet pour un système de financement en mutation

Un recours accru au financement par les marchés suppose pour les collectivités territoriales une communication financière sur Internet. Une évaluation des pratiques actuelles des collectivités émettrices et non émettrices selon une double méthode - scoring et analyse textuelle - révèle peu de différences significatives dans le contenu et l’utilisation du Web. Une plus grande interactivité est préconisée. Un clivage « communication budgétaire/financière » émerge pour expliquer les divergences dans l’exploitation des potentialités d’Internet.For local governments, increasing capital market financing implies financial communication on the Internet. The assessment of the current practices (i.e. scoring and textual analysis) of bond issuers and non-issuers reveals few significant differences in the content and the use of the Web. Greater interactivity is recommended. A split between budgetary and financial communication tends to explain the differences in exploiting the Web’s potential

Communication financière des collectivités locales françaises et crise internationale : des pratiques en mutation

La crise internationale a frappé les budgets des collectivités locales françaises et leur encours de dettes, notamment via les produits structurés. Il est alors légitime de s’interroger sur l’impact de cette crise sur leur communication financière. Cette recherche consiste en une analyse textuelle du contenu des rapports annuels ou financiers, par le logiciel Alceste. Une discussion des résultats au regard de la littérature sur les stratégies de communication fait apparaitre 2008, comme une année de bouleversements et dessine un cheminement allant de la « reconnaissance » au « changement ».The international crisis has affected budgets of French local governments and their debts, particularly through structured products. It’s well-founded to wonder about the impact of this crisis on their financial communication. This research is a textual analysis of the content of annual or financial reports by Alceste software. Discussing results based on a literature survey on communication strategies brings up 2008 as a year of confusion and highlights a shift from “recognition” to “change”