CMM-Bionature Seminar on Natural Resources

Térence Bayen and Antoine Rousseau will lecture conferences on this important topic.

Program

10h30 – Térence Bayen

ANALYSIS OF AN OPTIMAL CONTROL PROBLEM CONNECTED TO BIOPROCESSES INVOLVING A SATURATED SINGULAR ARC

Summary:

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 arc which is non-necessary admissible everywhere (i.e. the singular control can take values outside the admissible control set). Thanks to Pontrygin’s Principle, we provide an optimal synthesis of the problem that exhibits a frame point at the intersection of the singular arc and a switching curve. Numerical simulations allow to compute this curve and the frame point.

11h30 – Antoine Rousseau

Bioremediation of natural resources: how optimization and numerical simulations can help?

Summary:

In this lecture I will show how to combine numerical schemes and adjustement of systems of PDEs and ODEs to provide efficient feedback strategies for the biological decontamination of water resources. We will see how the model reduction may impact (or not) the quality of the model outputs. This work has been done with Alain Rapaport (INRA, France). In a second part I would like to address a few questions related to the underlying modeling issues (questions raised with V. Riquelme and H. Ramirez), and introduce the future work of Loïc Dagnas (Inria Chile and Ecole des Ponts) on the simulation of humedales in Chile.