Scopus İndeksli Yayınlar Koleksiyonu

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Now showing 1 - 9 of 9
  • Article
    Citation - WoS: 1
    Citation - Scopus: 1
    Sustainable Management of a Renewable Fishery Resource With Depensation Dynamics From a Control Systems Perspective
    (Gazi Univ, 2022) Cıfdaloz, Oguzhan
    Human societies are exploiting natural renewable sources such as fisheries, forests, groundwater basins, rivers, and soil at an increasing intensity. Around the world, these resources are being managed by various institutions or governments. One of the challenges faced by institutions is to develop strategies and policies to effectively manage these renewable resources under social and ecological uncertainties, disturbances, policy implementation difficulties, and measurement errors. In this paper, a fishery is considered as an example and the problem of managing a fishery is approached from a control systems perspective. The justification behind this approach is due to the observation that the problem of managing a renewable resource can be posed as a control systems problem and that the discipline of control systems possesses tools and methods to deal with model uncertainties, external disturbances, measurement errors and implementation issues. For the fishery, a depensation type population dynamics model is considered. Depensatory models are used in social/ecological systems in order to model dynamics of certain species of fish populations. An optimal control strategy based on Pontryagin’s Maximum Principle is derived and its sustainability and robustness properties with respect to parametric uncertainties, measurement errors and disturbances are examined. Finally, a sub-optimal but more robust control strategy is proposed and its robustness properties are provided. The main objective of the paper is to show that a control systems engineering approach can be applied to a social-ecological problem and it can provide easy to implement management strategies, insight, and guidance into the management of renewable resources. 
  • Article
    Citation - WoS: 22
    Citation - Scopus: 25
    Optimal Control Model for the Transmission of Novel Covid-19
    (Tech Science Press, 2021) Nasidi, Bashir Ahmad; Baleanu, Dumitru; Baba, Isa Abdullahi
    As the corona virus (COVID-19) pandemic ravages socio-economic activities in addition to devastating infectious and fatal consequences, optimal control strategy is an effective measure that neutralizes the scourge to its lowest ebb. In this paper, we present a mathematical model for the dynamics of COVID-19, and then we added an optimal control function to the model in order to effectively control the outbreak. We incorporate three main control efforts (isolation, quarantine and hospitalization) into the model aimed at controlling the spread of the pandemic. These efforts are further subdivided into five functions; u(1)(t) (isolation of the susceptible communities), u(2)(t) (contact track measure by which susceptible individuals with contact history are quarantined), u(3)(t) (contact track measure by which infected individualsare quarantined), u(4)(t) (control effort of hospitalizing the infected I-1) and u(5)(t) (control effort of hospitalizing the infected I-2). We establish the existence of the optimal control and also its characterization by applying Pontryaging maximum principle. The disease free equilibrium solution (DFE) is found to be locally asymptotically stable and subsequently we used it to obtain the key parameter; basic reproduction number. We constructed Lyapunov function to which global stability of the solutions is established. Numerical simulations show how adopting the available control measures optimally, will drastically reduce the infectious populations.
  • Article
    Citation - WoS: 101
    Citation - Scopus: 115
    On a Nonlinear Dynamical System With Both Chaotic and Nonchaotic Behaviors: a New Fractional Analysis and Control
    (Springer, 2021) Jajarmi, Amin; Defterli, Ozlem; Baleanu, Dumitru; Sajjadi, Samaneh Sadat
    In this paper, we aim to analyze the complicated dynamical motion of a quarter-car suspension system with a sinusoidal road excitation force. First, we consider a new mathematical model in the form of fractional-order differential equations. In the proposed model, we apply the Caputo-Fabrizio fractional operator with exponential kernel. Then to solve the related equations, we suggest a quadratic numerical method and prove its stability and convergence. A deep investigation in the framework of time-domain response and phase-portrait shows that both the chaotic and nonchaotic behaviors of the considered system can be identified by the fractional-order mathematical model. Finally, we present a state-feedback controller and a chaos optimal control to overcome the system chaotic oscillations. Simulation results demonstrate the effectiveness of the proposed modeling and control strategies.
  • Article
    Citation - WoS: 3
    Citation - Scopus: 5
    A Mathematical Model To Optimize the Available Control Measures of
    (Elsevier, 2021) Nasidi, Bashir Ahmad; Baleanu, Dumitru; Saadi, Sultan Hamed; Baba, Isa Abdullahi
    In the absence of valid medicine or vaccine for treating the pandemic Coronavirus (COVID-19) infection, other control strategies like; quarantine, social distancing, self- isolation, sanitation and use of personal protective equipment are effective tool used to prevent and curtail the spread of the disease. In this paper, we present a mathematical model to study the dynamics of COVID-19. We then formulate an optimal control problem with the aim to study the most effective control strategies to prevent the proliferation of the disease. The existence of an optimal control function is established and the Pontryagin maximum principle is applied for the characterization of the controller. The equilibrium solutions (DFE & endemic) are found to be locally asymptotically stable and subsequently the basic reproduction number is obtained. Numerical simulations are carried out to support the analytic results and to explicitly show the significance of the control. It is shown that Quarantine/isolating those infected with the disease is the best control measure at the moment.
  • Article
    Citation - WoS: 88
    Citation - Scopus: 94
    New Aspects of Time Fractional Optimal Control Problems Within Operators With Nonsingular Kernel
    (Amer inst Mathematical Sciences-aims, 2020) Jajarmi, Amin; Yildiz, Burak; Baleanu, Dumitru; Yildiz, Tugba Akman
    This paper deals with a new formulation of time fractional optimal control problems governed by Caputo-Fabrizio (CF) fractional derivative. The optimality system for this problem is derived, which contains the forward and backward fractional differential equations in the sense of CF. These equations are then expressed in terms of Volterra integrals and also solved by a new numerical scheme based on approximating the Volterra integrals. The linear rate of convergence for this method is also justified theoretically. We present three illustrative examples to show the performance of this method. These examples also test the contribution of using CF derivative for dynamical constraints and we observe the efficiency of this new approach compared to the classical version of fractional operators.
  • Article
    Citation - WoS: 166
    Citation - Scopus: 179
    A Survey on Fuzzy Fractional Differential and Optimal Control Nonlocal Evolution Equations
    (Elsevier, 2018) Baleanu, Dumitru; Nieto, Juan J.; Torres, Delfim F. M.; Zhou, Yong; Agarwal, Ravi P.
    We survey some representative results on fuzzy fractional differential equations, controllability, approximate controllability, optimal control, and optimal feedback control for several different kinds of fractional evolution equations. Optimality and relaxation of multiple control problems, described by nonlinear fractional differential equations with nonlocal control conditions in Banach spaces, are considered. (C) 2017 Elsevier B.V. All rights reserved.
  • Article
    Citation - WoS: 28
    Citation - Scopus: 34
    Optimal Chemotherapy and Immunotherapy Schedules for a Cancer-Obesity Model With Caputo Time Fractional Derivative
    (Wiley, 2018) Arshad, Sadia; Baleanu, Dumitru; Akman Yildiz, Tugba
    This work presents a new mathematical model to depict the effect of obesity on cancerous tumor growth when chemotherapy and immunotherapy have been administered. We consider an optimal control problem to destroy the tumor population and minimize the drug dose over a finite time interval. The constraint is a model including tumor cells, immune cells, fat cells, and chemotherapeutic and immunotherapeutic drug concentrations with the Caputo time fractional derivative. We investigate the existence and stability of the equilibrium points, namely, tumor-free equilibrium and coexisting equilibrium, analytically. We discretize the cancer-obesity model using the L1 method. Simulation results of the proposed model are presented to compare three different treatment strategies: chemotherapy, immunotherapy, and their combination. In addition, we investigate the effect of the differentiation order alpha and the value of the decay rate of the amount of chemotherapeutic drug to the value of the cost functional. We find out the optimal treatment schedule in case of chemotherapy and immunotherapy.
  • Article
    Citation - WoS: 12
    Citation - Scopus: 23
    Low-Regret Control for a Fractional Wave Equation With Incomplete Data
    (Springeropen, 2016) Joseph, Claire; Mophou, Gisele; Baleanu, Dumitru
    We investigate in this manuscript an optimal control problem for a fractional wave equation involving the fractional Riemann-Liouville derivative and with missing initial condition. For this purpose, we use the concept of no-regret and low-regret controls. Assuming that the missing datum belongs to a certain space we show the existence and the uniqueness of the low-regret control. Besides, its convergence to the no-regret control is discussed together with the optimality system describing the no-regret control.
  • Article
    Citation - WoS: 20
    Citation - Scopus: 23
    A Numerical Scheme for Two-Dimensional Optimal Control Problems With Memory Effect
    (Pergamon-elsevier Science Ltd, 2010) Defterli, Ozlem
    A new formulation for multi-dimensional fractional optimal control problems is presented in this article. The fractional derivatives which are coming from the formulation of the problem are defined in the Riemann-Liouville sense. Some terminal conditions are imposed on the state and control variables whose dimensions need not be the same. A numerical scheme is described by using the Grunwald-Letnikov definition to approximate the Riemann-Liouville Fractional Derivatives. The set of fractional differential equations, which are obtained after the discretization of the time domain, are solved within the Grunwald-Letnikov approximation to obtain the state and the control variable numerically. A two-dimensional fractional optimal control problem is studied as an example to demonstrate the performance of the scheme. (C) 2009 Elsevier Ltd. All rights reserved.