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Motion planning for the heat equation
SUMMARYThe paper gives an explicit open-loop control, able to approximately steer the one-dimensional heatequationwith control onthe boundaryfromanystate to any otherstate. The controlisobtainedExpand
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Mathematical modelling of carbohydrate degradation by human colonic microbiota.
The human colon is an anaerobic ecosystem that remains largely unexplored as a result of its limited accessibility and its complexity. Mathematical models can play a central role for a better insightExpand
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Motion planning for a class of partial differential equations with boundary control
We study the heat equation with one space dimension and control on the boundary. We give an explicit parametrization of the trajectories as a power series in the space variable with coefficientsExpand
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La notion de platitude aete bien definie et largement etudiee pour les systemes dynamiques de dimension finie. Une des consequences marquantes de cette propriete est de permettre la parametrisationExpand
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Impact of the Dairy Matrix Structure on Milk Protein Digestion Kinetics: Mechanistic Modelling Based on Mini-pig In Vivo Data
Beyond the individual content in nutrients, it is now established that the matrix structure is also to consider when evaluating the nutritional properties and possible health effects of a foodExpand
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Flatness-based control of PER protein oscillations in a drosophila model
We show how classical nonlinear control techniques such as bifurcation analysis and flatness-based motion planning can be applied to biological system models to bring a fast and systematic way to help designing chronomodulated therapeutics. Expand
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The heat treatment and the gelation are strong determinants of the kinetics of milk proteins digestion and of the peripheral availability of amino acids.
This study aimed to determine the kinetics of milk protein digestion and amino acid absorption after ingestion of four dairy matrices by six minipigs: unheated or heated skim milk and correspondingExpand
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Kinetic modelling of lactate utilization and butyrate production by key human colonic bacterial species.
Butyrate is the preferred energy source for colonocytes and has an important role in gut health; in contrast, accumulation of high concentrations of lactate is detrimental to gut health. The majorExpand
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Acid and rennet gels exhibit strong differences in the kinetics of milk protein digestion and amino acid bioavailability.
This study aimed at determining the kinetics of milk protein digestion and amino acid absorption after ingestion by six multi-canulated mini-pigs of two gelled dairy matrices having the sameExpand
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A mathematical model of the cell cycle and its control
We consider mathematical models for the cell cycle, i.e. the sequence of events that leads to mitosis, at the level of a population of cells. These are structured population Partial DifferentialExpand
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