Adaptive synchronization of uncertain fractionalorder. It consists of 30 original contributions written by eminent scientists and active researchers in the. Fuzzy controlbased synchronization of fractionalorder. A linearizing feedback technique has successfully been applied on this chaotic system. As an active research area, chaos synchronization with fractional calculus has received increasing attention in recent years due to its potentials in both theory and applications 1825. The chaotic dynamics of fractionalorder systems has attracted much attention recently. Synchronization of two fractionalorder chaotic systems. Control and switching synchronization of fractional order chaotic. In both control and synchronization, numerical simulations show the efficiency of the proposed methods. Synchronization control of fractionalorder discretetime chaotic systems xiaozhong liao, zhe gao and hong huang abstract this paper investigates the bifurcation phenomenon of fractionalorder discretetime chaotic systems and proposes the nonlinear control to synchronize two fractionalorder discretetime chaotic systems. Synchronization of fractionalorder chaotic systems with. Chaos, control, and synchronization in some fractional.
The control and synchronization technique, based on stability theory of fractionalorder systems, is simple and theoretically rigorous. Fractional order control and synchronization of chaotic. A survey of numerical simulations for multistrain tuberculosis models of fractional order and their optimal control 4. Synchronization of uncertain fractionalorder duffing. Predictionbased feedback control and synchronization algorithm of fractionalorder chaotic systems article pdf available in nonlinear dynamics 854 may 2016 with 94 reads how we measure reads. Control and synchronization of the financial systems with fractionalorder are discussed in this paper. Modified function projective lag synchronization in.
In addition, this paper presents the concept of synchronization of different fractional order chaotic systems using active control technique. In this paper, we introduce a threedimensional fractionalorder chaotic system. Synchronization of fractionalorder different memristor. Utilizing an approximation approach of fractional operator, the. Pdf fractional order control and synchronization of. Control and synchronization of chaotic fractionalorder coullet system via active controller m. Index termselnino system, fractional derivative, nonlinear control method, stability analysis. The fractionalorder operator is the generalization of integerorder operator. The synchronization problem of fractionalorder chaotic systems is.
In this article we utilize active control technique to synchronize different fractional order chaotic dynamical systems. Synchronization control of fractionalorder discretetime. In this article, an adaptive nonlinear controller is designed to synchronize two uncertain fractionalorder chaotic systems using fractionalorder sliding mode control. The present paper deals with fractionalorder version of a dynamical system introduced by chongxin et al. Synchronization of fractionalorder hyperchaotic systems. We investigate the chaos synchronization of two identical systems via a suitable linear controller applied to the response system.
Adaptive impulsive synchronization for a class of delay. The controller structure and adaptation laws are chosen such that asymptotic stability of. Dynamics, circuit design, synchronization and fractionalorder form of a noequilibrium chaotic system 2. This paper is concerned with the adaptive impulsive synchronization for a class of delay fractionalorder chaotic system. Robust synchronization of fractionalorder uncertain. Control and switching synchronization of fractional order chaotic systems using active control technique. The important finding by analysis is that the position of signal x 3 descends at the speed of 1 c as the parameter b increases, and the signal amplitude of x 1, x 2 can be. This chapter addresses the fuzzy adaptive controller design for the generalized projective synchronization gps of incommensurate fractionalorder chaotic. Synchronization of different order chaotic systems. However, since the topic of fractional discrete calculus is still new, to the best of our knowledge, very few fractional order chaotic maps have been proposed in the literature such as 18,19,20,21. Control and switching synchronization of fractional order.
Secondly, by constructing the suitable response system, the original fractional. Fractional order chaotic systems file exchange matlab. To control and synchronization of chaotic fractionalorder system an active sliding mode controller asmc is proposed. Synchronization of chaotic fractional order systems. It consists of 30 original contributions written by eminent scientists and active researchers in the field that address theories, methods and applications in a number of research areas related to fractional order control and synchronization of chaotic systems, such as. Pdf control and synchronization of chaotic fractionalorder. To achieve synchronization, an active control technique is used. Synchronization of fractional order chaotic systems. In this paper, a novel modified function projective lag synchronization mfpls for fractionalorder chaotic hyperchaotic systems is proposed. The comparison of time of synchronization when the systems pair approaches from standard order to fractional order is the key feature of the article. Control and synchronization of chaotic fractionalorder. Considering fractional derivatives do not satisfy the leibniz product rule, as it is known in integerorder calculus, it is difficult to achieve the synchronization with a scaling function between the. Control and switching synchronization of fractional order chaotic systems using active control technique a. An active control technique is applied to control this chaotic system.
Exploring the dynamics feature of robust chaotic system is an attractive yet recent topic of interest. Robust synchronization of fractionalorder chaotic systems at a prespecified. This toolbox contains the functions which can be used to simulate some of the wellknown fractional order chaotic systems, such as. This work is concerned with the synchronization of fractionalorder discretetime chaotic systems with different dimensions. However,tothebestofourknowledge,thereislittlework in the literature on finitetime control for fractionalorder chaotic systems which combines the nonsingular terminal. Pdf the book reports on the latest advances in and applications of fractional order control and synchronization of chaotic systems, explaining. Read advances in synchronization of coupled fractional. Pdf advanced synchronization control and bifurcation of.
Synchronization of chaotic fractionalorder windmi systems. Moreover, projective synchronization control of the fractionalorder hyperchaotic complex lu system is studied based on feedback technique and the stability theorem of fractionalorder systems, the scheme of antisynchronization for the fractionalorder hyperchaotic complex lu system is presented. When talking about chaotic systems in general, two of the main concerns are their control and synchronization. A fractional integral fi sliding surface is proposed for synchronizing the uncertain fractionalorder system, and then the sliding mode control technique is carried. The book reports on the latest advances in and applications of fractional order control and synchronization of chaotic systems, explaining the concepts involved in a clear, matteroffact style. Fractionalorder models for hiv viral and epidemiological. Firstly, according to the impulsive differential equations theory and the adaptive control theory, the adaptive impulsive controller and the parametric update law are designed, respectively.
Fpga implementation of fractional order chaotic systems 3. Synchronization of fractionalorder discretetime chaotic. Recent advances in chaotic systems and synchronization in this chapter a fractionalorder fo hybrid synchronization hs for n multiple hyperchaotic systems is achieved the hs between n systems coupled with ring connection is resolved when the first system couples the nth one the second system couples the first one and so on until the nth hyperchaotic system couples the nth. In this paper, based on the laplace transform theory, the conditions for achieving synchronization of different fractional order timedelay chaotic systems are analyzed by use of active control technique. In this article, synchronization of two different fractionalorder memristorbased chaotic systems is considered. Pdf fractional order control and synchronization of chaotic. The fractionalorder modeling and synchronization of electrically coupled neuron systems. Naturally, the synchronization of fractional order chaotic systems becomes a topic. This paper mainly focuses on the robust synchronization issue for driveresponse fractionalorder chaotic systems focs when they have unknown parameters and external disturbances. Composite learning sliding mode synchronization of chaotic. In this paper, tensor product tp model transformation. Chaotic synchronization of fractionalorder systems is further studied in this paper.
Ieeecaa journal of automatica sinica 1 fractionalorder control for a novel chaotic system without equilibrium shuyi shao and mou chen member, ieee, abstractthe control problem is discussed for a chaotic sys tem without equilibrium in this paper. The effectiveness and applicability of the sliding mode. Chaos control and synchronization in fractionalorder lorenzlike. Four different synchronization cases are introduced based on the switching parameters. The main proof is concerned with the problem of synchronization of memristorbased lorenz systems with. This type of controller is also applied to synchronize chaotic fractionalorder systems in. Recently, synchronization in discretetime chaotic systems attract more and more attentions and has been extensively studied, due to its potential applications in secure communication. Robust synchronization of chaotic systems with fractional order with adaptive fuzzy sliding mode control toktam motamedifar.
Based on the stability theory of fractionalorder differential equations, routhhurwitz stability condition, and by using linear control, simpler controllers are designed to achieve control and synchronization of the fractionalorder financial systems. A novel lmibased stabilization condition for fractionalorder tp models with a parallel distributed compensation pdc controller is. Robust synchronization of chaotic systems with fractional. Advanced synchronization control and bifurcation of chaotic fractional order systems is a scholarly publication that explores new developments related to novel chaotic fractional order systems. Then numerical simulations are provided to verify the effectiveness and. Synchronization of different fractional order chaotic.
Due to the existence of chaos in real practical systems and many applications in physics and engineering fields, control and synchronization of fractionalorder chaotic systems have attracted the attention of many researchers in the past few years 1115. There are three commonly used definition of the fractionalorder differential operator. In order to achieve the goal, the sliding mode control scheme only using output information is designed, and at the same time, the structures of a sliding mode surface and a sliding mode controller are also. The unstable equilibrium points of the fractionalorder lorenz chaotic system can be controlled via fractionalorder derivative, and chaos synchronization for the fractionalorder lorenz chaotic system can be achieved via fractionalorder derivative. In this work, a sliding mode control smc method and a composite learning smc clsmc method are proposed to solve the synchronization problem of cha. Neural adaptive quantized outputfeedback control based. Adaptive synchronization of fractionalorder memristor. Control and synchronization of the fractionalorder lorenz. This paper presents tp model transformationbased control and synchronization of a class of fractionalorder chaotic systems. In this letter, we study the synchronization of fractional order chaotic systems also.
Also, the static and dynamic synchronizations can be obtained when the switching parameters are functions of time. It has been found that the solution of many fractional. Some work has been done in the field of the chaos and control in fractional order systems, including chua system 1, fractional order chen system 2, fractional order lorenz system 3, fractional order rossle r. Synchronization between fractional order lorenz stenflo. Adaptive fractionalorder control for synchronization of. Adaptive synchronization of uncertain fractional order. Synchronization of chaotic fractionalorder chenlusystems via. Abstract in this paper, the issue of chaos control and synchronization problems of two systems of fractional order with adaptive fuzzy sliding model has been. Because the analysis of fractional order systems is not sufficient at present, we will numerically investigate this topic here. Adaptive synchronisation of fractionalorder chaotic systems. Synchronization of chaotic fractionalorder systems via linear control 83 the laplace transform of caputo fractional derivative requires the knowledge of the bounded initial values of the function and of its integer derivatives of order k 1,2. Recently, synchronization of chaotic fractionalorder systems starts to attract increasing attention due to its potential applications in secure communication and control processing matignon, 1996.
Tensor product model transformation based control and. Synchronization between fractionalorder chaotic systems and. Synchronization of fractional order chaotic dynamical systems is receiving increasing attention owing to its interesting applications in secure communications of analog and digital signals and cryptographic systems. The results show that designing appropriate control law and sliding.
Synchronization of fractionalorder chaotic systems was. Pdf control and synchronization of fractionalorder. Synchronization of different fractional order timedelay. Synchronization of fractionalorder chaotic systems using. This paper propose fractionalorder lu complex system. Hashim b a engineering mathematics, faculty of engineering, cairo university, egypt b school of mathematical sciences, universiti kebangsaan malaysia, selangor, malaysia. Fractional order control and synchronization of chaotic systems. Based on the idea of tracking control and stability theory of fractionalorder systems, a controller is designed to synchronize the fractionalorder chaotic system.