Browsing by Author "Mazenc, F."
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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 Dynamic output feedback stabilization of switched linear systems with delay via a trajectory based approach(Elsevier, 2018) Ahmed, Saeed; Mazenc, F.; Özbay, HitayA new technique is proposed to construct observers and to achieve output feedback stabilization of a class of continuous-time switched linear systems with a time-varying delay in the output. The delay is a piecewise continuous bounded function of time and no constraint is imposed on the delay derivative. For stability analysis, an extension of a recent trajectory based approach is used; this is fundamentally different from classical Lyapunov function based methods. A stability condition is given in terms of the upper bound on the time-varying delay to ensure global uniform exponential stability of the switched feedback system. The main result applies in cases where some of the subsystems of the switched system are not stabilizable and not detectable.Item Open Access Finite time estimation for time-varying systems with delay in the measurements(Elsevier, 2019) Ahmed, Saeed; Malisoff, M.; Mazenc, F.We build finite time observers for time-varying nonlinear systems with delays in the outputs, using a dynamic extension that computes fundamental matrices. Our observers achieve finite time convergence when no disturbances are present. When disturbances are present, we provide approximate values for the solutions, which lead to an upper bound on the approximation error after a suitable finite time. We illustrate our work in a class of systems arising in the study of vibrating membranes, where time-varying coefficients can be used to represent intermittent measurements.Item Open Access Finite time estimation through a continuous-discrete observer(John Wiley and Sons, 2018) Mazenc, F.; Ahmed, S.; Malisoff, M.We study two broad classes of nonlinear time-varying continuous-time systems with outputs. For the first class, we build an observer in the case where a state dependent disturbance affects the linear approximation. When the disturbances are the zero functions, our observer provides exact values of the state at all times larger than a suitable finite time, and it provides an approximate estimate when there are nonzero disturbances, so our observers are called finite time observers. We use this construction, which is of interest for its own sake, to design a globally exponentially stabilizing dynamic output feedback for a family of nonlinear systems whose outputs are only available on some finite time intervals. Our simulations illustrate the efficacy of our methods.Item Open Access Finite time estimation via piecewise constant measurements⁎(Elsevier B.V., 2018) Mazenc, F.; Ahmed, S.We study a broad class of linear continuous-time time-varying systems that contain piecewise continuous disturbances and piecewise constant outputs. Under an observability assumption, we construct a new type of observer to estimate the state of the system in a predetermined finite time in the presence of the disturbances. In contrast to the well-established finite time observer design techniques which estimate the system state using a continuous output, our proposed observer only requires a piecewise constant output. Our simulations illustrate the efficacy of our observer.Item Open Access Output feedback stabilization by reduced order finite time observers using a trajectory based approach(IEEE, 2019) Malisoff, M.; Mazenc, F.; Ahmed, SaeedWe use finite time reduced order continuous-discrete observers to solve an output feedback stabilization problem for a class of nonlinear time-varying systems whose outputs contain uncertainty. Unlike earlier works, our feedback is discontinuous, but it does not contain distributed control terms. Our trajectory based approach is based on a contractivity condition. We illustrate our control in the context of a tracking problem for nonholonomic systems in chained form.Item Open Access Reduced order finite time observers for time-varying nonlinear systems(Institute of Electrical and Electronics Engineers Inc., 2019) Mazenc, F.; Ahmed, Saeed; Malisoff, M.; Teel, A. R.; Egerstedt, M.We build reduced order finite time observers for a large class of nonlinear time-varying continuous-time systems. We illustrate our results using a tracking problem for nonholonomic systems in chained form.Item Open Access Stability analysis of switched systems with time-varying discontinuous delays(IEEE, 2017) Mazenc, F.; Malisoff, M.; Özbay, HitayA new technique is proposed to ensure global asymptotic stability for nonlinear switched time-varying systems with time-varying discontinuous delays. It uses an adaptation of Halanay's inequality to switched systems and a recent trajectory based technique. The result is applied to a family of linear time-varying systems with time-varying delays.Item Open Access Stability and robustness analysis for switched systems with time-varying delays(Society for Industrial and Applied Mathematics Publications, 2018) Mazenc, F.; Malisoff, M.; Özbay, HitayA new technique is presented for the stability and robustness analysis of nonlinear switched time-varying systems with uncertainties and time-varying delays. The delays are allowed to be discontinuous (but are required to be piecewise continuous) and arbitrarily long with known upper bounds. The technique uses an adaptation of Halanay’s inequality and a trajectory-based technique, and is used for designing switched controllers to stabilize linear time-varying systems with time-varying delays.Item Open Access State feedback stabilization of switched systems with delay: trajectory based approach(IEEE, 2017) Mazenc, F.; Ahmed, Saeed; Özbay, HitayWe present a new trajectory based approach for state feedback stabilization of switched linear continuous-time systems with a time-varying input delay. In contrast with finding classical common Lyapunov function or multiple Lyapunov functions for establishing the stability of the closed-loop switched system, the new trajectory based approach relies on verifying certain inequalities along the solution of a supplementary system. This study does not make any assumption regarding the stabilizability of all of the constituent subsystems of the switched system. Moreover, no assumption is needed about the differentiability of the delay and no constraint is imposed on the upper bound of the delay derivative. Finally, an illustrative example is included to illustrate the applicability of our results.