Andrei Halanay

Andrei Halanay
Polytechnic University of Bucharest | UPB · Department of mathematics and informatics

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95
Publications
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526
Citations
Citations since 2016
18 Research Items
276 Citations
201620172018201920202021202201020304050
201620172018201920202021202201020304050
201620172018201920202021202201020304050
201620172018201920202021202201020304050

Publications

Publications (95)
Article
Full-text available
In this paper, a complex system of delay differential equations modeling malaria evolution under treatment and considering the immune response, is introduced. The existence of the equilibrium points is investigated and the stability properties of the steady state representing the most aggravated phase of the disease are investigated, following a Ly...
Article
Full-text available
In this paper the stability of the zero equilibrium of a system with time delay is studied. The critical case of a multiple zero root of the characteristic equation of the linearized system is treated by applying a Malkin type theorem and using a complete Lyapunov-Krasovskii functional. An application to a model for malaria under treatment consider...
Article
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ShareLink https://www.tandfonline.com/eprint/5VPGYGJHTY7UPZ5UQRM7/full?target=10.1080/00207179.2020.1862423
Article
In this paper the stability of an equilibrium of a feedback nonlinear system with time delay and structural switching is studied. The critical case of a zero root of the characteristic equations of the linearized systems is treated by applying a Malkin type theorem using a complete Lyapunov-Krasovskii functional.
Article
We introduce a mathematical model which captures the cellular evolution in the case of patients diagnosed with acute lymphoblastic leukemia and who are under maintenance therapy. We develop the model using a system of delay-differential equations. The main goal of this paper is to describe the complex biological model by considering three different...
Conference Paper
We study the stability of limit cycles that appear due to a constant delay introduced in the control of an unmanned vehicle. Stability switches of the equilibrium point shows the existence of a Hopf bifurcation. For the delay differential equations with constant delay, we establish the formulae required to calculate the Lyapunov coefficient and det...
Presentation
Full-text available
control time delay; electrohydraulic servomechanism
Presentation
Full-text available
mathematical models, time delay, hydraulic servomechanism
Article
The complex model of cells evolution in leukemia considers the competition between the populations of healthy and leukemic cells, the asym- metric division and the immune system's action in response to the disease. Delay differential equations are used to describe the dynamics of healthy and leukemic cells in case of CML (Chronic Myeloid Leukemia)....
Article
The problem of modeling hydraulic servomechanisms as systems with time delay is less researched, although the input-output time delay is herein objective and, in fact, real in every system which involves load dynamics. The objective of this paper is to propose a few types of delay differential equations which characterize the dynamics of the hydrau...
Article
Full-text available
The paper presents the stability analysis of the equilibria in a longitudinal flight of an unmanned aircraft with constant forward velocity. The motion of the aircraft is described using delay differential equations with constant delays, the delay being considered in flight control compartment. The goal is to study the effects of the delays for the...
Conference Paper
We capture the evolution in competition of healthy and leukemic cells in Chronic Myelogenous Leukemia (CML) taking into consideration the response of the immune system. Delay-differential equations in a Mackey-Glass approach are used. We start with the study of stability of the equilibrium points of the system. Conditions on parameters for the loca...
Conference Paper
The paper aims to study the dynamic behavior of a speed governor for a hydraulic turbine using a mathematical model. The nonlinear mathematical model proposed consists in a system of delay differential equations (DDE) to be compared with already established mathematical models of ordinary differential equations (ODE). A new kind of nonlinearity is...
Conference Paper
We consider a system of nonlinear delay differential equations that describes the interaction between three competing cell populations: healthy, leukemic and anti-leukemia T cells involved in Chronic Myeloid Leukemia (CML) under treatment with Imatinib. The aim of this work is to establish which model parameters are the most important in the succes...
Article
Full-text available
We use fictitious domain method with penalization for the Stokes equation in order to obtain approximate solutions in a fixed larger domain including the domain occupied by the structure. The coefficients of the fluid problem, excepting the penalizing term, are independent of the deformation of the structure. It is easy to check the inf-sup conditi...
Conference Paper
This paper investigates an optimal control problem associated with a complex nonlinear system of multiple delay differential equations modeling the development of healthy and leukemic cell populations incorporating the immune system. The model takes into account space competition between normal cells and leukemic cells at two phases of the developm...
Conference Paper
Full-text available
We prove that the domain obtained by small perturbation of a Lipschtz domain is the union of a star-shaped domains with respect to every point of balls, such that the radius of the balls is independent of the perturbation. This result is useful in order to get uniform estimation for a fluid-structure interaction problem.
Article
We analyse the stability properties of a steady state in a complex, strongly nonlinear, system of delay-differential equations with multiple delays, modelling an aggravated phase of cell evolution in Chronic Myelogenous Leukemia. The competition on space between healthy and leukemic cell populations is taken into consideration. Three types of divis...
Article
Full-text available
The paper is devoted to the study of a mathematical model of drug therapy for Chronic Myelogenous Leukemia (CML). The disease dynamics are given by a couple of delay differential equations that describe the interaction between a stem-like population of CML cells and a more mature, differentiated one, without self-renewal properties. A molecular tar...
Conference Paper
The complex model studied in this paper considers the competition between the populations of healthy and leukemic stem-like short-term and mature leukocytes and the influence of the T-lymphocytes on the evolution of leukemia. Delay differential equations with delay-dependent parameters are used in a modified Mackey-Glass approach, with the consider...
Article
This paper introduces a complex model that describes the competition between the populations of healthy and leukemic cells and the inuence of the T-lymphocytes on the evolution of leukemia. The system consists of 5 delay differential equations derived from a Mackey-Glass approach. The main results of this work center around suffcient linear stabili...
Conference Paper
The evolution of leukemia is modeled with a delay differential equation model of four cell populations: two populations (healthy and leukemic) ) of stem-like cells involving a larger category consisting of proliferating stem and progenitor cells with self-renew capacity and two populations (healthy and leukemic) of mature cells, considering the com...
Conference Paper
Starting from a mathematical model which describes the dynamics of Chronic Myelogenous Leukemia (CML) when the action of different cell lines of the immune system is considered, the aim of the paper is to analyze the parameters influence in CML evolution. The model consists of seven delay differential equations with seven delays. The physiological...
Conference Paper
A mathematical model, coupling the dynamics of short-term stem-like cells and mature leukocytes in leukemia with that of the immune system, is investigated. The model is described by a system of nine delay differential equations with nine delays. Three equilibrium points E 0 , E 1 , E 2 are highlighted. The stability and the existence o...
Conference Paper
The dynamics and evolution of leukemia is determined by the interactions between normal and leukemic cells populations at every phase of the development of hematopoietic cells. For both types of cell populations, two subpopulations are considered, namely the stem-like cell population (i.e. with unlimited self-renew ability) and a more mature, diffe...
Conference Paper
Full-text available
We present a formulation for a steady fluid-structure interaction problem using fictitious domain technique with penalization. Numerical results are presented. © IFIP International Federation for Information Processing 2014.
Article
We study a mathematical model describing the dynamics of leukemic and normal cell populations (stem-like and differentiated) in chronic myeloid leukemia (CML). This model is a system of four delay differential equations incorporating three types of cell division. The competition between normal and leukemic stem cell populations for the common micro...
Article
A two dimensional two-delays differential system modeling the dynamics of stem-like cells and white-blood cells in Chronic Myelogenous Leukemia under treatment is considered. Stability of equilibria is investigated and emergence of periodic solutions of limit cycle type, as a result of a Hopf bifurcation, is eventually shown. All three types of ste...
Data
In this paper we consider the heat equation with memory in a bounded region Ω ⊂ R d , d ≥ 1, in the case that the propagation speed of the signal is infinite (i.e. the Colemann-Gurtin model). The memory kernel is of class C 1 . We examine its controllability properties both under the action of boundary controls or when the controls are distributed...
Article
Full-text available
In this paper we consider the heat equation with memory in a bounded region $\Omega \subset\mathbb{R}^d$, $d\geq 1$, in the case that the propagation speed of the signal is infinite (i.e. the Colemann-Gurtin model). The memory kernel is of class $C^1$. We examine its controllability properties both under the action of boundary controls or when the...
Article
A two dimensional two-delays differential system modeling the dynamics of stem-like cells and white-blood cells in Chronic Myelogenous Leukemia is considered. All three types of stem cell division (asymmetric division, symmetric renewal and symmetric differentiation) are present in the model. Stability of equilibria is investigated and emergence of...
Article
A mathematical model, coupling the dynamics of short-term stem-like cells and mature leukocytes in leukemia with that of the immune system, is investigated. The model is described by a system of seven delay differential equations with seven delays. Three equilibrium points E0, E 1, E2 are highlighted. The stability and the existence of the Hopf bif...
Article
Full-text available
We use the boundary feedback control introduced in V. Barbu [”Boundary stabilization of equilibrium solutions to parabolic equations”, IEEE Trans. Automat. Control 58, 2416-2420 (2013)], in order to stabilize an unstable heat equation in two dimensions. We propose two numerical algorithms. The feedback boundary condition is treated explicitly in th...
Article
Full-text available
Control synthesis for electrohydraulic servoactuators (EHSA) is achieved using elements of geometric control theory. Based on a Malkin type theorem for switched systems of ordinary differential equations, the existence of stabilizing feedback controllers is prove to hold in the specific case of EHSAs when the relative degree of the nonlinear contro...
Article
Full-text available
In the present paper, we use a penalization of the Stokes equation in order to obtain approximate solutions in a larger domain including the domain occupied by the structure. The coefficients of the fluid problem, excepting the penalizing term, are constant and independent of the deformation of the structure, which represents an advantage of this a...
Article
Full-text available
Heat equations with memory of Gurtin-Pipkin type have controllability properties which strongly resemble those of the wave equation. Instead, recent counterexamples show that when the laplacian appears also out of the memory term, the control properties do not parallel those of the (memoryless) heat equation, in the sense that there are $L^2$-initi...
Article
Some nonlinear control laws for a fifth order mathematical model, representative for an electrohydraulic servomechanism (EHS), are presented in the paper. Intrinsically, the EHS mathematical model has several shortcomings: critical case for stability, relative degree defect, and switching type nonsmooth nonlinearity. First, the control synthesis is...
Article
Some nonlinear control laws for a fifth order mathematical model, representative for an electrohydraulic servomechanism (EHS), are presented in the paper. Intrinsically, the EHS mathematical model has several shortcomings: critical case for stability, relative degree defect, and switching type nonsmooth nonlinearity. First, the control synthesis is...
Conference Paper
Full-text available
We present a weak formulation for a steady fluid-structure interaction problem using an embedding domain technique with penalization. Except of the penalizing term, the coefficients of the fluid problem are constant and independent of the deformation of the structure, which represents an advantage of this approach. A second advantage of this model...
Conference Paper
Full-text available
The paper aims to illustrate the algorithm developed in the paper [6] in some specific problems of shape optimization issued from fluid mechanics. Using the fictitious domain method with penalization, the fluid equations will be solved in a fixed domain. The admissible shapes are parametrized by continuous function defined in the fixed domain, then...
Article
Full-text available
A one-dimensional delay differential equation modeling leukemia under treatment is investigated to decide over the stability of equilibria and existence of Hopf bifurcations. All three types of stem cell devision (asymmetric division, symmetric renewal and symmetric differentiation) are considered. The effect of drug resistance is considered throug...
Conference Paper
A mathematical model for the dynamics of leukemic cells during treatment is introduced. Delay differential equations are used to model cells' evolution and are based on the Mackey-Glass approach, incorporating Goldie-Coldman law. Since resistance is propagated by cells that have the capacity of self-renewal, a population of stem-like cells is...
Article
The paper is devoted to the study of PIO (pilot induced oscillations) in a longitudinal flight. The phenomenon of PIO is the interaction between aircraft's motion and the pilot. PIO are present more often in terminal flight conditions. Using the qualitative theory of delay differential equations, a conventional time-delay model is considered and th...
Article
Electro-hydraulic servomechanisms (EHSM) are important components of flight control systems and their role is to control the movement of the flying control surfaces in response to the movement of the cockpit controls. As flight-control systems, the EHSMs have a fast dynamic response, a high power to inertia ratio and high control accuracy. The pape...
Article
A mathematical model for the study of the dynamics of Chronic Myelogenous Leukemia is developed. It takes into consideration the asymmetric division of Stem-like cells and the anti-leukemia immune response, focused on the dynamics of CD8+ cytotoxic T-cells. On the lines in the works of Kim et al ([7], [8]) the model can be used to better understand...
Article
Full-text available
A model for the evolution of short-term hematopoietic stem cells and of leukocytes in leucemia under periodic treatment is introduced. It consists of a system of periodic delay differential equations and takes into consideration the asymmetric division. A guiding function is used, together with a theorem of Krasnoselskii, to prove the existence of...
Article
Full-text available
We consider a model for the heat equation with memory, which has infinite propagation speed, like the standard heat equation. We prove that, in spite of this, for every $ T>0 $ there exist square integrable initial data which cannot be steered to hit zero at time $ T $, using square integrable controls. We show that the counterexample we present c...
Article
Existence and stability of periodic solutions are studied for a system of delay differential equations with two delays and with periodic coefficients. It models the evolution of hematopoietic stem cells and mature neutrophil cells in chronic myelogenous leukemia under a periodic treatment that acts only on mature cells. Existence of a guiding funct...
Article
Full-text available
The main result of the paper is a suffcient condition for existence of controllers that stabilize the zero solution for some switched nonlinear control systems in the critical case of a zero eigenvalue in the spectrum of the Jacobian matrix calculated in zero. The control synthesis is based on a condition on the relative degree in the equilibrium p...
Article
Full-text available
The paper is devoted to the study of pilot induced oscillations in the landing transition between the approach task and flare to touch-down. These oscillations are proved to appear in a longitudinal flight model when the delay in pilot’s reactions exceeds a certain threshold for which the stability of equilibria is lost and a Hopf bifurcation appea...
Article
Full-text available
Existence of periodic motions in a roll-coupling model of an aircraft under the action of a periodic force due to gravitational terms is investigated. Some general sufficient conditions for exponential asymptotic stability of such a periodic solution are deduced and applied to a particular case.
Article
A periodic treatment is incorporated in a two-phase model of evolution of hematopoietic stem cells in blood diseases. Stability of the zero solution is discussed.
Article
Full-text available
Consideration of the effects of the mounting structure stiffness on electrohydraulic servomechanisms actuating primary flight controls yields a switched control system of seven nonlinear differential equations. The stabilizing control synthesis has to cope with the critical case of a zero eigenvalue of the Jacobian matrices calculated in equilibria...
Article
Full-text available
Existence and stability of periodic solutions is analyzed first for the mathematical model of the Glasgow osteosarcome at mice subject to periodic treatment. The same properties are investigated for a two-phase stem cell dynamics model in hematological diseases.
Chapter
Full-text available
To a pump controlled electrohydraulic actuator, a mathematical model consisting of a switching nonlinear control system of ordinary differential equations is applied. In the study of stability of equilibria, the critical case of a zero eigenvalue in the spectrum of the Jacobian matrix is encountered. The approach in the Lyapunov-Malkin Theorem, tog...
Conference Paper
Inspired by Clairambault et al. (2003) a treatment scheme is associated to the model of evolution of hematopoietic pluripotent stem cells in cyclical blood diseases studied in Colijn and Mackey (2005a,b); Haurie et al. (1998); Mackey (1978, 1979). It is proved that a nonzero positive periodic solution exists and its stability is investigated.
Article
Full-text available
Stability of the zero solution is analyzed for a family of switched systems indexed by a parameter, each system having λ = 0 in the spectrum of the Jacobian matrix calculated in zero. It is proved that existence of a common quadratic Lyapunov function for some lower dimensional linear systems is sufficient to ensure local uniform stability of the z...
Article
The effects of mounting structure stiffness on mechano-hydraulic servomechanisms actuating aircraft primary flight controls are modeled by a six-dimensional nonlinear system of ordinary differential equations. Stability analysis of equilibria reveals the presence of a critical case that is handled through the use of the Lyapunov–Malkin theorem. Sta...
Article
This work discusses geometric optimization problems governed by stationary Navier-Stokes equations. Optimal domains are proved to exist under the assumption that the family of admissible domains is bounded and satisfies the Lipschitz condition with a uniform constant, and in the absence of the uniqueness property for the state system. Through the p...
Article
Full-text available
The mounting structure stiffness's effects on mecanohy-draulic servomechanisms actuating aicraft's primary flight controls are mod-eled as a system of ordinary differential equations. Stability analysis of equi-libria reveals the presence of a critical case that is handled through the use of the Lyapunov-Malkin theorem. Stability charts are drawn u...
Conference Paper
Full-text available
Abstract – A five-dimensional nonlinear mathematical model of the electrohydraulic servo(mechanism) is considered. In the system equilibria analysis, the critical case of a zero eigenvalue occurs. The Lyapunov-Malkin Theorem and Routh-Hurwitz criterion provide conditions for controllers to stabilize all relevant equilibria in the closed-loop system...
Article
Full-text available
The mathematical model of an electrohydraulic servomechanism is developed and a theorem on the stability of equilibria is proved. AMS 2000 Subject Classification: 70K20, 93D05, 93D15. Key words: Lyapunov stability, critical case, Lyapunov-Malkin Theorem.
Article
The mathematical model of an electrohydraulic servomechanism is developed and a theorem on the stability of equilibria is proved. AMS 2000 Subject Classification: 70K20, 93D05, 93D15. Key words: Lyapunov stability, critical case, Lyapunov-Malkin Theorem.
Article
We prove that, although unstable by Lyapunov, the equlibrium (N-0, 0, 0) in the plankton population model given in [1] is stable with respect to a relevant set of solutions. This clarifies and completes the considerations in [2].
Article
The mathematical model of an electrohydraulic servomechanism is developed and a theorem on the stability of equilibria is proved. AMS 2000 Subject Classification: 70K20, 93D05, 93D15. Key words: Lyapunov stability, critical case, Lyapunov-Malkin Theorem.
Conference Paper
Full-text available
The dynamics of an electrohydraulic servo actuating aircraft’s primary flight controls is modelled with consideration of mounting structure’s stiffness effect.Acontrol lawis synthesised using the backstepping method and Barbalat’s lemma to ensure the asympotic tracking of reference signals.
Article
This paper is devoted to the study of the stability of limit cycles of a nonlinear delay differential equation with a distributed delay. The equation arises from a model of population dynamics describing the evolution of a pluripotent stem cells population. We study the local asymptotic stability of the unique nontrivial equilibrium of the delay eq...
Article
For control systems that model electro-hydraulic servo-actuators, the possibility of stabilization by a linear stationary feedback low is analysed. It is also shown that, when this is possible, equilibria exhibit also asymptotic stability with respect to some relevant state variables.
Article
Full-text available
Starting from plysical laws a four-dimensional nonlinear model for mecano-hydraulic servomechanisms is deduced. The stability of its equilibria is analysed using a theorem of Lyapunov and Malkin to handle the critical case due to the presence of zero in the spectrum of the matrix of the linear part around equilibria. Stability diagrams are drawn an...
Conference Paper
Full-text available
For a mechanohydraulic servomechanism used in the control chain of an airplane a mathematical model given by four strongly nonlinear ordinary differential equations is considered. It relates the state variables of the inertial load (position and speed) to the pressures in the two chambers of the hydrocylinder. The Jacobian matrix for the quilibria...
Article
For separable Hilbert spaces ℱ, ℱ * and Θ∈H ∞ (D 2 ,ℒ(ℱ,ℱ * )), ∥Θ∥ ∞ ≤1, Θ left-inner, define ℋ=ℋ(Θ)=H 2 (D 2 ,ℱ * )⊖ΘH 2 (D 2 ,ℱ) and then A=P ℋ M z | ℋ , T=P ℋ M ξ | ℋ with M z , M ξ operators of multiplication with independent variables. Suppose that σ re (Θ)={(λ,μ)∈D 2 |∃ an orthonormal sequence {e n } n in ℱ * such that lim n→∞ ∥Θ(λ,μ) * e n...
Article
It is proved that the equilibrium point (N 0, 0, 0) for the plankton population model given in Edwards and Brindley, (19961. Edwards , A. M. and Brindley , J. 1996 . Oscillatory behaviour in a three-component plankton population model. Dynamics and Stability of Systems , 11 ( 4 ) : 347 – 370 . [Taylor & Francis Online], [Web of Science ®]View all r...
Article
We prove that if a hydraulic copying servomechanism subject to a periodic cutting force has as an input a combination of step, ramp, and sin and cos functions then an output of the same form (normal motion) exists under certain constraints. We investigate the stability of the normal motion by the Lyapunov-Malkin methods as the value of the underlap...
Article
A model of a hydraulic copying system in the space-state form is given and the analytic study of stability is performed. When h, the underlap of the servoventil of the hydraulic amplifier is chosen as a parameter, a critical value h 0 is determined so that for h>h 0 the equilibrium is asymptotically stable. Using the Hopf bifurcation theorem a stab...
Article
An analytical study of stability is made for a hydromechanical servomechanism used in copying systems. In the framework of a nonlinear system of ODE mathematically modelling the servomechanism, we prove that for a ramp input the steady-state solution bifurcates into a stable limit cycle for a certain value of the underlap spool valve.
Article
Using the Hopf theorem and the algorithm developed in [1] we prove that while loosing asymptotic stability, a hydraulic copying system still works at a stable limit cycle. We compute the value of the underlap of the valve for this to happen and remark that it is in the range of turbulent oil flow.
Article
Let {xn}n be a normalised boundedly complete basic sequence in a Banach space E and let zn = xn + y n, n≥1, be a perturbation of {xn}n. Denote by F = [xn] and G = [zn] the closedsubspaces generated by {xn}n and {zn}n in E and let q:E → E/F be the quotient map. It is proved that if {yn}n satisfies the Paley-Wiener condition of stability and is weakl...
Article
Full-text available
Electrohydraulic servomechanisms considered in this paper are modeled by five-dimensional switched nonlinear systems of control differential equations. In the stability analysis of equilibria the critical case of a zero eigenvalue of the Jacobian matrix calculated in equilibria is encountered. Local coordinates transformation and the Lyapunov-Malki...
Article
The author’s previous results [Rev. Roum. Math. Pures Appl. 41, 51-82 (1996; Zbl 0872.47005)] are recovered under the condition that the essential resolvent rapidly grows near an arc on the unit circle, without any further assumptions on the spectrum.