Aghileh Heydari - Academia.edu (original) (raw)

Papers by Aghileh Heydari

In this paper, we propose the concept of partial stability instead of that of global stability to... more In this paper, we propose the concept of partial stability instead of that of global stability to deal with the stability issues of epidemic models. The partial stability is able to provide a more meaningful analysis of the problem since it only focuses on the behavior of some of the variables (infected and infectious) instead of the complete population. It has been shown that the vaccination free SEIR model can still be partially stable even when a globally stability property does not hold, for two types of nonlinear incidence rates. By introducing the concept of partial stability and by designing a control vaccination based on it. Guarantee the eradication of an epidemic disease without requiring the global stability of the epidemic model

Journal of Advances in Mathematics, 2012

In this paper, synchronization of heart follower oscillator which has lower frequency AV with hea... more In this paper, synchronization of heart follower oscillator which has lower frequency AV with heart leader oscillator which has dominant frequency SA will be studied. It can be seen if two nodes SA and AV are not synchronized, different types of cardiac blocking arrhythmias occur. Thus, in this paper, beside putting voltage to node SA, by applying time delay in bi-oscillator model of heart system and designing appropriate controller via linear and adaptive methods, we try to prevent blocking arrhythmias of heart. Finally, we apply Lyapanuv stability theorem for ensuring convergence.

Communications in Mathematical Analysis, 2016

In this paper we study the dynamics of Hepatitis B virus (HBV) infection under administration of ... more In this paper we study the dynamics of Hepatitis B virus (HBV) infection under administration of a vaccine and treatment, where the disease is transmitted directly from the parents to the offspring and also through contact with infective individuals. Stability of the disease-free steady state is investigated. The basic reproductive rate, R_0R_0R0, is derived. The results show that the dynamics of the model is completely determined by the basic reproductive number R0R_0R0. If R01R_0 1R_01, the disease-free equilibrium is unstable and the disease is uniformly persistent.

Journal of Advances in Mathematics, 2014

Approximate analytical solution of the matrix Riccati differential equation related to the linear... more Approximate analytical solution of the matrix Riccati differential equation related to the linear quadratic optimal control problems, is the main goal of this paper which has a specific importance in the optimal control theory. To this end, a modification of the parametric iteration method is used. This modification, reduces the time consuming repeated calculations and improves the convergence rate of the iterational algorithm. Comparison with the existent solutions and also with the numerical Runge-Kutta (RK78) method confirms the high accuracy of the method, whilst accessibility to the analytical solutions is the preference of the new technique.

In this article, a numerical approach for solving a class of nonlinear optimal control problems i... more In this article, a numerical approach for solving a class of nonlinear optimal control problems is presented. This approach is a combination of a spectral collocation method and the parametric iteration method. As will be shown, the proposed indirect strategy provides good approximations of all variables i.e. control, state and costate as opposed to the many direct methods. Several examples are considered to assess the accuracy and features of the presented method.

In this paper, we discuss the synchronization and anti-synchronization of two identical chaotic T... more In this paper, we discuss the synchronization and anti-synchronization of two identical chaotic T-systems. The adaptive and nonlinear control schemes are used for the synchronization and anti-synchronization. The stability of these schemes is derived by Lyapunov Stability Theorem. Firstly, the synchronization and anti-synchronization are applied to systems with known parameters, then to systems in which the drive and response systems have one unknown parameter. Numerical simulations show the effectiveness and feasibility of the proposed methods.

Iranian Journal of Fuzzy Systems, 2011

In this paper, a model of an optimal control problem with chance constraints is introduced. The p... more In this paper, a model of an optimal control problem with chance constraints is introduced. The parameters of the constraints are fuzzy, ran- dom or fuzzy random variables. To defuzzify the constraints, we consider possibility levels. By chance-constrained programming the chance constraints are converted to crisp constraints which are neither fuzzy nor stochastic and then the resulting classical optimal control problem with crisp constraints is solved by the Pontryagin Minimum Principle and Kuhn-Tucker conditions. The model is illustrated by two numerical examples.

In this paper, a two-phase algorithm, namely IVNS, is proposed for solving nonlinear optimal cont... more In this paper, a two-phase algorithm, namely IVNS, is proposed for solving nonlinear optimal control problems. In each phase of the algorithm, we use a variable neighborhood search (VNS), which performs a uniform distribution in the shaking step and the successive quadratic programming, as the local search step. In the first phase, VNS starts with a completely random initial solution of control input values. To increase the accuracy of the solution obtained from the phase 1, some new time nodes are added and the values of the new control inputs are estimated by spline interpolation. Next, in the second phase, VNS restarts by the solution constructed by the phase 1. The proposed algorithm is implemented on more than 20 well-known benchmarks and real world problems, then the results are compared with some recently proposed algorithms. The numerical results show that IVNS can find the best solution on 84% of test problems. Also, to compare the IVNS with a common VNS (when the number of...

International Journal of Infection, 2019

Background: A correct diagnosis of a disease among several diseases with the same clinical sympto... more Background: A correct diagnosis of a disease among several diseases with the same clinical symptoms is very important and is a difficult task in medical science. Misdiagnosis of these diseases in the short term causes very high and serious damage to the health of patients and usually results in loss of golden time. Objectives: In this paper, our purpose is to achieve the best conclusion, which contributes to the diagnosis of the critical illness without losing the golden opportunity based on clinical data and using mathematical models, especially fuzzy mathematics. Methods: The data regarding patient's signs and symptoms were collected in the hospitals. We attained the best choice of diseases among the considered options of diseases by using basic fuzzy rules, fuzzy control techniques, fuzzy mathematics and fuzzy systems. To write the basic fuzzy rules, the information that we used was adopted by experts in infectious diseases or data records of patients who reached a definite diagnosis of disease by various tests. Then, by using these rules, the system of mathematical equations was formed. By solving this system, coefficients of a linear equation were estimated witch its values according to the clinical signs of a patient indicates the probability that the patient will be infected with that disease. In this process, the number of patients studied is n not effective. But the more patients are studied, the more accurately the coefficients of the diagnosis equation are obtained. Results: The symptoms of some patients whose disease have been definitely diagnosed were used as inputs of the system of our equations and it was observed that the system's outputs approximately coincide the exact diagnosis of the disease, which indicates that the equations obtained for the diagnosis of diseases are acceptable. Conclusions: The findings of this study can help to correctly diagnose the disease without losing golden opportunities. We hope that using the results of this research, the error in the initial diagnosis of diseases is significantly reduced.

Journal of Control, Automation and Electrical Systems, 2016

In this paper, an optimal adaptive sliding mode controller is proposed for anti-synchronization o... more In this paper, an optimal adaptive sliding mode controller is proposed for anti-synchronization of two identical hyperchaotic systems. We use hyperchaotic complex T-system for master and slave systems with unknown parameters in the slave system. To construct the optimal adaptive sliding mode controller, first a simple sliding surface is designed. Then, the optimal adaptive sliding mode controller is derived to guarantee the occurrence of the sliding motion. Also, suitable update laws are designed to estimate the unknown parameters. The optimality and stability of the proposed method are proved using Hamilton-Jacobi-Bellman(HJB) technique and Barbalates lemma, respectively. Finally, antisynchronization result is applied to secure communication via masking method. Numerical simulations illustrate the ability and effectiveness of proposed method.

International Journal of Applied Mathematical Research, 2015

Parametric iteration method falls under the category of the analytic approximate methods for solv... more Parametric iteration method falls under the category of the analytic approximate methods for solving various kinds of nonlinear differential equations. Its convergence only for some special problems has been proved. However in this paper, an analysis of error is presented, then due to it, the convergence of method for general problems is proved. To assess the performance of the claimed error bound and also the convergence of the method, numerical experiments are presented performed in MATLAB 2012b.

Mathematical Problems in Engineering, 2015

Here, a two-phase algorithm is proposed for solving bounded continuous-time nonlinear optimal con... more Here, a two-phase algorithm is proposed for solving bounded continuous-time nonlinear optimal control problems (NOCP). In each phase of the algorithm, a modified hybrid genetic algorithm (MHGA) is applied, which performs a local search on offsprings. In first phase, a random initial population of control input values in time nodes is constructed. Next, MHGA starts with this population. After phase 1, to achieve more accurate solutions, the number of time nodes is increased. The values of the associated new control inputs are estimated by Linear interpolation (LI) or Spline interpolation (SI), using the curves obtained from the phase 1. In addition, to maintain the diversity in the population, some additional individuals are added randomly. Next, in the second phase, MHGA restarts with the new population constructed by above procedure and tries to improve the obtained solutions at the end of phase 1. We implement our proposed algorithm on 20 well-known benchmark and real world proble...

ISRN Applied Mathematics, 2014

If theSAandAVoscillators are not synchronized, it may arise some kinds of blocking arrhythmias in... more If theSAandAVoscillators are not synchronized, it may arise some kinds of blocking arrhythmias in the system of heart. In this paper, in order to examine the heart system more precisely, we apply the three-oscillator model of the heart system, and to prevent arrhythmias, perform the following steps. Firstly, we add a voltage with ranga1andωfrequency toSAnode. Then, we use delay time factor in oscillators and finally the appropriate control is designed. In this paper, we have explained how simulating and curing these arrhythmias are possible by designing a three-oscillator system for heart in the state of delay and without delay and by applying an appropriate control. In the end, we present the simulation results.

Applied Mathematics, 2013

Computational and Mathematical Methods in Medicine, 2014

Hepatitis B virus (HBV) infection is a worldwide public health problem. In this paper, we study t... more Hepatitis B virus (HBV) infection is a worldwide public health problem. In this paper, we study the dynamics of hepatitis B virus (HBV) infection which can be controlled by vaccination as well as treatment. Initially we consider constant controls for both vaccination and treatment. In the constant controls case, by determining the basic reproduction number, we study the existence and stability of the disease-free and endemic steady-state solutions of the model. Next, we take the controls as time and formulate the appropriate optimal control problem and obtain the optimal control strategy to minimize both the number of infectious humans and the associated costs. Finally at the end numerical simulation results show that optimal combination of vaccination and treatment is the most effective way to control hepatitis B virus infection.

Computational Methods for Differential Equations, 2014

In this paper we introduce a numerical approach that solves optimal control problems (OCPs) using... more In this paper we introduce a numerical approach that solves optimal control problems (OCPs) using collocation methods. This approach is based upon B-spline functions. The derivative matrices between any two families of B-spline functions are utilized to reduce the solution of OCPs to the solution of nonlinear optimization problems. Numerical experiments conrm our theoretical ndings.

IMA Journal of Mathematical Control and Information, 2016

Optimal control problems for a class of time delay systems with quadratic performance index are s... more Optimal control problems for a class of time delay systems with quadratic performance index are studied. By approximating various time functions in the systems as their truncated hybrid functions, we attain to algebraic equations. The properties of these hybrid functions including block-pulse functions and Bernstein polynomials are explained. Operational matrices of the hybrid functions are used to transform the solution of optimal control problem to the solution of algebraic equations. To demonstrate the validity and applicability of the method, some examples are presented.

Journal of Mathematics and Computer Science

This work presents an approximate solution method for the linear time-varying multi-delay systems... more This work presents an approximate solution method for the linear time-varying multi-delay systems and time delay logistic equation using variational iteration method. The method is based on the use of Lagrange multiplier for identification of optimal value of a parameter in a functional. This procedure is a powerful tool for solving large amount of problems. Also, it provides a sequence which converges to the solution of the problem without discretization of the variables. In this study, an idea is proposed that accelerates the convergence of the sequence which results from the variational iteration formula for solving systems of delay differential equations. Illustrative examples are included to demonstrate the validity and applicability of the technique.

International Journal of Industrial Electronics, Control and Optimization (IECO), 2022

These days analysis and research about the nonlinear fractional system (NFS)s in the presence of ... more These days analysis and research about the nonlinear fractional system (NFS)s in the presence of uncertainty and external disturbance is one of the most critical problems in the control field. This paper investigates the asymptotic stabilization of a class of NFS while the upper bound of uncertainty and external disturbance are unknown. To do this, first, a fractional-integral sliding surface is constructed. After that, a new robust adaptive fractional sliding mode controller (RAFSMC) is designed, which is robust against the model uncertainties and external disturbances. The unknown upper bound of uncertainties and disturbances is estimated by a stable adaptive law. The Lyapunov stability theorem is used for stability analysis of the designed controller. Finally, the proposed method is applied to two practical examples, the glucose-insulin and the Lu systems. The simulation results are provided to show the effectiveness of the proposed methodology. These examples show rapid convergence to the equilibrium point with low chattering.