MAIRET , Francis

In this work, we study a minimal time control problem for a perfectly mixed continuous culture with n ≥ 2 species and one limiting resource. The model that we consider includes a mutation factor for the microorganisms. Our aim is to provide optimal feedback control laws to optimize the selection of the species of interest. Thanks to...

The design of control laws for bioprocesses are generally based on simplified single-species models. Biodiversity (made of a mixture of different species or strains) is nonetheless inherent in any artificial ecosystem in a bioreactor. Here we propose to define and study the robustness to biodiversity of bioprocess control laws: given a control...

Microalgae have recently attracted attention for their potential to produce high added compounds, proteins, and even biofuels. Our paper seeks to develop a control strategy for light-limited continuous culture imposing a stress for which microalgae have to adapt. This operating mode - called photoinhibistat - consists, for a culture with a...

Because of the inherent complexity of bioprocesses, mathematical models are more and 1 more used for process design, control and optimization etc... These models are generally 2 based on a set of biochemical reactions. Model equations are then derived from mass balance, 3 coupled to empirical kinetics. Biological models are nonlinear and...

We consider the problem of global stabilization of an unstable bioreactor model (e.g. for anaerobic digestion), when the measurements are discrete and in finite number (" quantized "), with control of the dilution rate. The measurements define regions in the state space, and they can be perfect or uncertain (i.e. without or with overlaps). We...

Mathematical modeling is becoming ever more important to assess the potential, guide the design, and enable the efficient operation and control of industrial-scale microalgae culture systems (MCS). The development of overall, inherently multiphysics, models involves coupling separate submodels of (i) the intrinsic biological properties,...

We propose metabolic models for the haptophyte microalgae Tisochrysis lutea with different possible organic carbon excretion mechanisms. These models—based on the DRUM (Dynamic Reduction of Unbalanced Metabolism) methodology—are calibrated with an experiment of nitrogen starvation under day/night cycles, and then validated with nitrogen-limited...

This paper is devoted to the study of an optimal control problem for a fed-batch bioreactor with one species and one substrate. Our objective is to obtain an optimal feedback control, steering the system in minimal time to a given target defined by conditions on the substrate concentration and the volume of the reactor. The novelty in this work...

Microalgae can be cultivated in closed or open photobioreactors (PBR). In these systems, light rapidly decreases as it passes through the culture due to the turbidity of the medium. Thus, microalgae experiment different light intensities depending on their position in the medium. In this paper, we study theoretically how the growth rate of...

The periodically forced light-limited Droop model represents microalgae growth under co-limitation by light and a single substrate, accounting for periodic fluctuations of factors such as light and temperature. In this paper, we describe the global dynamics of this model, considering general monotone growth and uptake rate functions. Our main...

Outdoor microalgae cultures can undergo a photoinhibitory process that can result in a loss in biomass productivity. This loss can be reduced by shading the culture such that the incident photon flux decreases. Based on a simple model of light-limited growth, we look for a control strategy to shadow the culture in order to maximize the biomass...

This 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...

Light supply is one of the most important parameters to be considered for enhancing microalgae growth in photobioreactors (PBR) with artificial light. However, most of the mathematical works do not consider incident light as a parameter to be optimized. In this work based on a simple model of light-limited growth, we determine optimal values...

Light supply is one of the most important parameters to be considered for enhancing microalgae growth in photobioreactors (PBR) with artificial light. However, most of the mathematical works do not consider incident light as a parameter to be optimized. In this work based on a simple model of light-limited growth, we determine optimal values...

Understanding adaptation of bacterial growth for a changing environment is a fundamental biological problem which also has a great interest from the biotechnological point of view. This paper extends one of existing bacterial growth models by taking macromolecular degradation into account and provides new mathematical results. The related...

The light attenuation factor, defined by the ratio between the incident light and the light at the bottom of the reactor, is a key operating parameter for light-limited phototrophic culture. Here, two nonlinear control laws have been proposed in order to regulate this ratio: a static controller, which is input-to-state stable with respect to...

For both fundamental biology and engineering applications, it is relevant to investigate how microorganisms adapt to changing environmental conditions. In this work, we consider a continuous-timedynamic problem of resource allocation between metabolic and gene expression machineries for a self-replicating prokaryotic cell population. In...

We design a simple model of the growth ofpolysaccharide-decomposing bacteria in a continuous stirredtank reactor. We control the dilution rate to optimize the outputof monosaccharides, which is of industrial interest. We studythe model, find the optimum at the stationary state, and designa control that makes the closed system globally stable...

Phytoplankton are key components of ecosystems. Their growth is deeply influenced by temperature. In a context of global change, it is important to precisely estimate the impact of temperature on these organisms at different spatial and temporal scales. Here, we review the existing deterministic models used to represent the effect of...

Microalgae cultivation with wastewater is a promising way of reducing the energetic needs for wastewater treatment and the costs of biofuel production. However, the very turbid medium is not favorable for the development of microalgae. Indeed, light, the key element for photosynthesis, rapidly vanishes along depth due to absorption and...

We design a simple model of the growth of polymer-decomposing bacteria in a continuous stirred tank reactor. The dilution rate is controled to optimize the output of monomers. This model is studied in order to find the optimum at the stationary state. However, the optimal stationary state is not robust against perturbations, leading to washout...

Although the effect of temperature on microbial growth has been widely studied, the role of proteome allocation in bringing about temperature-induced changes remains elusive. To tackle this problem, we propose a coarse-grained model of microbial growth, including the processes of temperature-sensitive protein unfolding and chaperone-assisted...

In this work, we study the coupling of a culture of microalgae 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...

No description

Microorganisms have evolved complex strategies for controlling the distribution of available resources over cellular functions. Biotechnology aims at interfering with these strategies, so as to optimize the production of metabo-lites and other compounds of interest, by (re)engineering the underlying regulatory networks of the cell. The...