Browsing by Author "Bonnet, C."
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Item Open Access A practical cell density stabilization technique through drug infusions: a simple pathfinding approach(IEEE - Institute of Electrical and Electronics Engineers, 2023-07-17) Djema, W.; Bonnet, C.; Özbay, Hitay; Mazenc, F.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 involving nodes and edges. Each node stands for a full-fledged nonlinear system with distributed delays where the parameters are constant. For each node, a stable positive steady state may exist. In the network framework, a change in the growth-factor concentration is interpreted as a transition from one node to another. The objective is then to determine the best switching signal steering the biological parameters over time, making the overall dynamic system moving from one operating mode to another, until reaching a desired stable state. Our method provides a (sub)optimal therapeutic strategy, guiding the density of cells from an abnormal state towards a healthy one, through multiple drug infusions. The drug sequence is deduced from the optimal switching signal provided by a classical pathfinding algorithm, associated with the network representation.Item Open Access Analysis of blood cell production under growth factors switching(Elsevier B.V., 2017) Djema, W.; Özbay, Hitay; Bonnet, C.; Fridman, E.; Mazenc, F.; Clairambault, J.Hematopoiesis is a highly complicated biological phenomenon. Improving its mathematical modeling and analysis are essential steps towards consolidating the common knowledge about mechanisms behind blood cells production. On the other hand, trying to deepen the mathematical modeling of this process has a cost and may be highly demanding in terms of mathematical analysis. In this paper, we propose to describe hematopoiesis under growth factor-dependent parameters as a switching system. Thus, we consider that different biological functions involved in hematopoiesis, including aging velocities, are controlled through multiple growth factors. Then we attempt a new approach in the framework of time-delay switching systems, in order to interpret the behavior of the system around its possible positive steady states. We start here with the study of a specific case in which switching is assumed to result from drug infusions. In a broader context, we expect that interpreting cell dynamics using switching systems leads to a good compromise between complexity of realistic models and their mathematical analysis. © 2017Item Open Access A coupled model for healthy and cancerous cells dynamics in Acute Myeloid Leukemia(IFAC, 2014) Avila, J. L.; Bonnet, C.; Özbay, Hitay; Clairambault, J.; Niculescu, S. I.; Hirsch, P.; Delhommeau, F.In this paper we propose a coupled model for healthy and cancerous cell dynamics in Acute Myeloid Leukemia. The PDE-based model is transformed to a nonlinear distributed delay system. For an equilibrium point of interest, necessary and sufficient conditions of local asymptotic stability are given. Simulation examples are given to illustrate the results.Item Open Access Local asymptotic stability conditions for the positive equilibrium of a system modeling cell dynamics in leukemia(Springer, Berlin, Heidelberg, 2012) Özbay, Hitay; Bonnet, C.; Benjelloun H.; Clairambault J.A distributed delay system with static nonlinearity has been considered in the literature to study the cell dynamics in leukemia. In this chapter local asymptotic stability conditions are derived for the positive equilibrium point of this nonlinear system. The stability conditions are expressed in terms of inequalities involving parameters of the system. These inequality conditions give guidelines for development of therapeutic actions. © 2012 Springer-Verlag GmbH Berlin Heidelberg.Item Open Access A new model of cell dynamics in Acute Myeloid Leukemia involving distributed delays(2012) Avila, J. L.; Bonnet, C.; Clairambault, J.; Özbay, Hitay; Niculescu, S. I.; Merhi, F.; Tang, R.; Marie, J. P.In this paper we propose a refined model for the dynamical cell behavior in Acute Myeloid Leukemia (AML) compared to (Özbay et al, 2012) and (Adimy et al, 2008).We separate the cell growth phase into a sequence of several sub-compartments. Then, with the help of the method of characteristics, we show that the overall dynamical system of equations can be reduced to two coupled nonlinear equations with four internal sub-systems involving distributed delays. © 2012 IFAC.Item Open Access A numerical method for stability windows and unstable root-locus calculation for linear fractional time-delay systems(Elsevier, 2012-08-14) Fioravanti, A.R.; Bonnet, C.; Özbay, Hitay; Niculescu, S. I.This paper aims to provide a numerical algorithm able to locate all unstable poles, and therefore the characterization of the stability as a function of the delay, for a class of linear fractional-order neutral systems with multiple commensurate delays. We start by giving the asymptotic position of the chains of poles and the conditions for their stability for a small delay. When these conditions are met, the root continuity argument and some simple substitutions allow us to determine the locations where some roots cross the imaginary axis, providing therefore the complete characterization of the stability windows. The same method can be extended to provide the position of all unstable poles as a function of the delay.Item Open Access PID controller design for fractional-order systems with time delays(Elsevier, 2011-11-22) Özbay, Hitay; Bonnet, C.; Fioravanti, A.R.Classical proper PID controllers are designed for linear time invariant plants whose transfer functions are rational functions of sα, where 0<α<1, and s is the Laplace transform variable. Effect of inputoutput time delay on the range of allowable controller parameters is investigated. The allowable PID controller parameters are determined from a small gain type of argument used earlier for finite dimensional plants.Item Open Access SOS methods for stability analysis of neutral differential systems(Springer, 2009) Peet, M. M.; Bonnet, C.; Özbay, HitayThis paper gives a description of how "sum-of-squares" (SOS) techniques can be used to check frequency-domain conditions for the stability of neutral differential systems. For delay-dependent stability, we adapt an approach of Zhang et al. [10] and show how the associated conditions can be expressed as the infeasibility of certain semialgebraic sets. For delay-independent stability, we propose an alternative method of reducing the problem to infeasibility of certain semialgebraic sets. Then, using Positivstellensatz results from semi-algebraic geometry, we convert these infeasibility conditions to feasibility problems using sum-of-squares variables. By bounding the degree of the variables and using the Matlab toolbox SOSTOOLS [7], these conditions can be checked using semidefinite programming.Item Open Access Stability analysis of cell dynamics in leukemia(E D P Sciences, 2012) Özbay, Hitay; Bonnet, C.; Benjelloun, H.; Clairambault, J.In order to better understand the dynamics of acute leukemia, and in particular to find theoretical conditions for the efficient delivery of drugs in acute myeloblastic leukemia, we investigate stability of a system modeling its cell dynamics. The overall system is a cascade connection of sub-systems consisting of distributed delays and static nonlinear feedbacks. Earlier results on local asymptotic stability are improved by the analysis of the linearized system around the positive equilibrium. For the nonlinear system, we derive stability conditions by using Popov, circle and nonlinear small gain criteria. The results are illustrated with numerical examples and simulations.Item Open Access Stability analysis of systems with distributed delays and application to hematopoietic cell maturation dynamics(IEEE, 2008-12) Özbay, Hitay; Bonnet, C.; Clairambault, J.We consider linear systems with distributed delays where delay kernels are assumed to be finite duration impulse responses of finite dimensional systems. We show that stability analysis for this class of systems can be reduced to stability analysis of linear systems with discrete delays, for which many algorithms are available in the literature. The results are illustrated on a mathematical model of hematopoietic cell maturation dynamics. © 2008 IEEE.Item Open Access Stability of fractional neutral systems with multiple delays and poles asymptotic to the imaginary axis(IEEE, 2010) Fioravanti, A. R.; Bonnet, C.; Özbay, HitayThis paper addresses the H∞-stability of linear fractional systems with multiple commensurate delays, including those with poles asymptotic to the imaginary axis. The asymptotic location of the neutral chains of poles are obtained, followed by the determination of conditions that guarantee a finite H∞ norm for those systems with all poles in the left half-plane of the complex plane.Item Open Access Stability windows and unstable root-loci for linear fractional time-delay systems(Elsevier, 2011) Fioravanti, A.R.; Bonnet, C.; Özbay, Hitay; Niculescu, S.-I.The main point of this paper is on the formulation of a numerical algorithm to find the location of all unstable poles, and therefore the characterization of the stability as a function of the delay, for a class of linear fractional-order neutral systems with multiple commensurate delays. We start by the asymptotic position of the chains of poles and conditions for their stability, for a small delay. When these conditions are met, we continue by means of the root continuity argument, and using a simple substitution, we can find all the locations where roots cross the imaginary axis. We can extend the method to provide the location of all unstable poles as a function of the delay. Before concluding, some examples are presented. © 2011 IFAC.