Optimized time-delayed feedback control of fractional chaotic oscillator with application to secure communications Amir Rikhtegar Ghiasi Faculty of electrical and computer engineering, University of Tabriz, Tabriz, Iran Email:agiasi@tabrizu.ac.ir Mona Saber Gharamaleki Faculty of electrical and computer engineering, University of Tabriz, Tabriz, Iran Email: m.saber96@ms.tabrizu.ac.ir Elaheh Mohammadi asl Khasraghi Faculty of electrical and computer engineering, University of Tabriz, Tabriz, Iran Email: elaheh.mhd96@ms.tabrizu.ac.ir Zahra Sattarzadeh Kalajahi Faculty of electrical and computer engineering, University of Tabriz, Tabriz, Iran Email: z.sattarzadeh96@ms.tabrizu.ac.ir Abstract—In this paper new type of time-delayed feedback control is designed based on particle swarm optimization method. This controller is used in the control of chaotic behavior of fractional order chaotic oscillator. Using a discretization method practical realization of the proposed system has been done. Also secure communication using the designed method is done. Simulation results show the performance of the designed controller. Keywords—Time-delayed feedback; Fractional-order; Chaotic oscillator; Particle swarm optimization; secure communications I. INTRODUCTION According to the chaotic behavior in many fields, study on this behavior is so important problem. Chaotic systems are unpredictable and this unpredictability has very application in many fields such as laser [1-2], biological systems[3] and secure communications [4]. Unpredictable behavior of these systems make control of these systems as a challenging problem. For the decades, studies on the control of chaotic systems have been done. In last decades, fractional version of chaotic systems have been expanded [5]. Fractional calculations are the general version of ordinary calculations, and according to the high accuracy on fractional order modeling of systems, this type of modeling has gained the great attractions. Especially on the chaotic systems, different types of fractional order systems are introduced [6-7]. Different types of controllers have been introduced according to this regard such as passive control [8-9] , feedback control[10], impulsive control[11] , and many others. The basic idea of these methods mostly obtained from two basic method: OGY method [12] and time delay feedback control [13]. Idea of time delay feedback control is add a control signal to the chaotic system to stabilize the system. This control signal is related to the present state and a delayed value of state. The main work in this method is to determine proper feedback gain and time delay to guarantee the stability of the chaotic system[18]. A new method to stabilize the chaotic behavior of fractional order system has been introduced, recently [5]. Fractional order makes chaotic system with much complexity. And control of this system becomes a challenging problem. In this paper this chaotic behavior on fractional order system has been controlled using the optimized time-delayed feedback which is the new point in the chaos control in the fractional order systems. The organization of this paper is as the follows: In section 2 basic relations about fractional calculations are introduced. Model of fractional order electrical chaotic system is shown in section 3. Section 4 describes the pervious studies on the time- delayed feedback control and optimized method. Practical implantation and simulation of the proposed introduced in section 5 and main conclusions of the paper are mentioned on section 6. II. FRACTIONAL ORDER SYSTEMS General forms of the fractional order operator have been defined in many studies [15]. One of the well known definitions is Riemann-Liouville definition as [16]:    () = 1 Γ(−)     ∫  () (−) −+1  0  (1) where n is an integer such that−1≤<. Laplace transform of fractional derivate is defined as [16]: {   ()} =   {()} − ∑ [ −1+ ()] =0 −1 =1 (2) where {} shows Laplace transform. For zero initial condition of fractional derivate of () Laplace transform of fractional derivative, operates as the integer one. 978-1-7281-1003-5/19/$31.00 ©2019 IEEE Authorized licensed use limited to: Universita degli Studi di Bologna. Downloaded on October 02,2024 at 11:54:49 UTC from IEEE Xplore. Restrictions apply.