Section: New Results

Other results

This section contains some theoretical as well as applied results, that are not directly connected to the main field of the team.

Theoretical ecology

Participant: Tewfik Sari.

In [24] , ecological trade-offs between species are studied to explain species coexistence in ecological communities. In our model, plant species compete for sites where each site has a fixed stress condition. Species differ both in stress tolerance and competitive ability. We derive the deterministic discrete-time dynamical system for the species abundances. We prove the conditions under which plant species can coexist in a stable equilibrium. We compare our model with a recently proposed, continuous-time dynamical system for a tolerance-fecundity trade-off in plant communities, and we show that this model is a special case of the continuous-time version of our model.

Calculus of variations

Participant: Térence Bayen.

The work [37] is devoted to the study of necessary and sufficient optimality conditions for weak and strong minima for optimal control problems governed by semi-linear parabolic equations; whereas in the field of calculus of variation, these conditions (such as Euler-Lagrange equation, Legendre's condition, Weierstrass's condition) have been deeply investigated, the study of strong solutions for optimal control problems of partial differential equations is new.

Ice cream crystallization

Participant: Céline Casenave.

We study the problem of the control of an ice cream crystallization process (the experimental pilot plant is located at Irstea Antony). The goal is to control the viscosity of the ice cream at the outlet of the continuous crystallizer. The problem has been studied in two steps.

Modeling, model reduction and parameter identification. On the basis of a population balance equation describing the evolution of the crystal size distribution (CSD) of the ice cream, and an energy balance equation, we have proposed an input-output reduced order model of the process, which is based on physical assumptions. The parameters of the model have been identified and the model has been validated from experimental data [68] .

Design of the control law. Based on the reduced order model, a nonlinear control strategy based on an adaptive linearizing control law coupled with a Smith predictor to account for the measurement delay has been proposed [41] , [66] , [67] . The control has been implemented (Labview-Matlab interface) and then validated on the experimental pilot plant. During the industrial conference which has been organized in February 2013 by the European CAFE project (see Section 8.3.1 ), and which representatives of several industries in food processing attended, a live demonstration of the designed control law has been performed.

This work was conducted as a part of the European CAFE project, described in Section 8.3.1 , in collaboration with CESAME (Univ. Catholique de Louvain-la-neuve), Irstea Antony and AgroParisTech.

Semi-Markov land use dynamic

Participant: Fabien Campillo, Angelo Raherinirina.

We pursued the development of semi-Markov model for the inference of land use dynamic from data proposed by IRD. The thesis of A. Raherinirina was defended in August 2013 [12] . Later in the year during the stay of A. Raherinirina in Montpellier we completed an article accepted by the journal ARIMA and that will be published in 2014 [17] .