DJEMA , Walid

An improved mathematical model describing the process of generating energy from household waste treatment is proposed and analyzed. It is a three-dimensional nonlinear system that illustrates the process of transforming household waste stored in a landfill into energy that flows to a user's network. More precisely, the state of the system...

In this work, we study the question of selecting in minimal-time a microalgae species of interest using the Droop model to describe the dynamics of two distinct populations competing for a limiting nutrient. This amounts to consider an optimal control problem governed by a five-dimensional affine control system in which the control is the...

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In a photobioreactor, due to the gradient of light, microalgae are successively exposed to conditions of low and high (inhibiting) light. This phenomenon can be captured by the Han model, which is a common mechanistic model of photoinhibition. Based on Han's description, we introduce a dynamic system of microalgae growth involving two control...

In this paper, we investigate the problem of species separation in minimal time. Droop model is considered to describe the evolution of two distinct populations of microorganisms that are in competition for the same resource in a photobioreactor. We focus on an optimal control problem (OCP) subject to a five-dimensional controlled system in...

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This paper proposes a strategy to separate two strains of microalgae in minimal time. The control is the dilution rate of the continuous photobioreactor. The microalgae dynamics is described by the Droop's model, taking into account the internal quota storage of the cells. Using Pontryagin's principle, we develop a dilution-based control...

We investigate a minimal-time control problem in a chemostat continuous photo-bioreactor model that describes the dynamics of two distinct microalgae populations. More precisely, our objective in this paper is to optimize the time of selection-or separation-between two species of microalgae. We focus in this work on Droop's model which takes...

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We present a simple mathematical model of ordinary differential equations that describes the interaction between a healthy cell population and cancerous cell population. This model includes the effects on cell populations of chemotherapy and targeted therapy, which are two bounded control variables. We study this model and seek to optimize the...

The paper focuses on a generic optimal control problem (OCP) deriving from the competition between two microbial populations in continuous cultures. The competition for nutrients is reduced to a two-dimensional dynamical nonlinear-system that can be derived from classical quota models. We investigate an OCP that achieves species separation over...

The paper focuses on a generic optimal control problem (OCP) deriving from the competition between two microbial populations in continuous cultures. The competition for nutrients is reduced to a two-dimensional dynamical nonlinear-system that can be derived from classical quota models. We investigate an OCP that achieves species separation...

We consider a nonlinear system with distributed delays modeling cell population dynamics, where the parameters depend on growth-factor concentrations. A change in one of the growth factor concentrations may lead to a switch in the corresponding model parameter. Our first objective is to achieve a network representation of the switching system...

This work is a first step towards a generic and highly flexible dynamical heat transfer model for unravelling the complex nonlinear dynamics of microalgae growing in different cultivation systems and under different climates. Physical models for predicting reactor temperature are crucial to simulate a wide range of scenarios and therefore for...

Microalgae cultivation for energy production is a promising avenue for converting solar light into sustainable biofuel. Solar processes are however subjected to the permanent fluctuations of light and medium temperature. Accurate temperature prediction of the culture medium turns out to be critical for optimising growth conditions. In this...

We want to reconcile some earlier mod-eling ways of the cell cycle in one common framework. Accordingly, we consider a model that contains a compartment where cells may be quiescent for an unlimited time, along with a proliferating phase in which most of the cells may divide, or die, while few of them may be arrested during their cycle for...

We study the optimization of resource allocation in bacteria evolving in periodic environments. We use a dynamical model of the metabolism of these microorganisms with a control variable representing the allocation of protein precursors. We mathematically define the objective of maximizing the long-term growth of a given cell. We carry out a...

We investigate optimization of an algal-bacterial consortium, where an exogenous control input modulates bacterial resource allocation between growth and synthesis of a resource that is limiting for algal growth. Maximization of algal biomass synthesis is pursued in a continuous bioreactor, with dilution rate as an additional control variable....

We consider the problem of maximization of metabolite production in bacterial cells formulated as a dynamical optimal control problem (DOCP). By Pontryagin's maximum principle, optimal solutions are concatenations of singular and bang arcs and exhibit the chattering or Fuller phenomenon, which is problematic for applications. To avoid...

As society transitions away from fossil fuels towards renewable energy sources, finding alternatives that are reliable becomes imperative. Waste-to-energy bioprocesses are promising options due to their ability to operate independently of weather conditions or time of day, making them sustainable and potentially lucrative solutions. This paper...

Microalgae are unicellular autotrophic organisms that have the potential to be used for various biotechnological applications like biofuel or wastewater treatment in large scale production systems. The dynamics of microalgae growth in outdoor systems are strongly dependent on light and temperature and thus on meteorology. In fact, they are the...

We consider the problem of maximization of metabolite production in bacterial cells. Numerical methods showed that the major phase of the solutions for different initial states and final times is the singular regime which exhibits a special structure reminiscent of the turnpike phenomenon. We prove that singular trajectories indeed have the...

Most eukaryotes inherit their mitochondria from only one of their parents. When there are different sexes, it is almost always the maternal mitochondria that are transmitted. Indeed, maternal uniparental inheritance has been reported for the brown alga Ectocarpus but we show in this study that different strains of Ectocarpus can exhibit...