Sharif Digital Repository

In this article by introducing and subsequently applying the Min-Max method, chaos has been suppressed in discrete time systems. By using this nonlinear technique, the chaotic behavior of Behrens-Feichtinger model is stabilized on its first and second-order unstable fixed points (UFP) in presence and absence of noise signal. In this step, a comparison has also been carried out among the proposed Min-Max controller and the Pyragas delayed feedback control method. Next, to reduce the computation required for controller design, the clustering method has been introduced as a quantization method in the Min-Max control approach. To improve the performance of the acquired controller through... 

In this Letter the impulsive synchronization of the Chen's hyperchaotic systems is discussed. Some new and sufficient conditions on varying impulsive distance are established in order to guarantee the synchronizabillity of the systems using the synchronization method. In particular, some simple conditions are derived in synchronizing the systems by equal impulsive distances. Two illustrative examples are provided to show the feasibility and the effectiveness of the proposed method. The boundaries of the stable regions are also estimated. © 2006 Elsevier B.V. All rights reserved  

oActive sliding mode control is one of the effective methods to synchronize chaotic systems in the presence of uncertainties. Use of the method, however, requires decision making on how to choose the control parameters for a specific performance. In this paper we propose an algorithm to determine the best control parameters for which the minimum control efforts are required to synchronize two identical or non-identical chaotic systems. We have also determined the maximum range of the uncertainties on which the selected control parameters to work properly. The effectiveness of the proposed method has been verified through numerical simulations  

In this paper, synchronization of chaotic systems with unknown parameters and unmeasured states is investigated. Two nonidentical chaotic systems in the framework of a master and a slave are considered for synchronization. It is assumed that both systems have uncertain dynamics, and states of the slave system are not measured. To tackle this challenging synchronization problem, a novel neural network-based adaptive observer and an adaptive controller have been designed. Moreover, a neural network is utilized to approximate the unknown dynamics of the slave system. The proposed method imposes neither restrictive assumption nor constraint on the dynamics of the systems. Furthermore, the... 

In this letter, it is shown that some of the equalities that were used in the proof of the main theorem of the paper given by Lin and Lee are not consistent with fractional calculus principles. Simple counterexamples are provided to confirm this point. Moreover, correct versions of equations that were derived in the mentioned theorem are presented. Based on these corrections, the synchronization scheme proposed in the mentioned paper is investigated  

Synchronization of two fractional order hyperchaotic systems considering uncertainties and sector nonlinear inputs is investigated in this paper. A new fractional order sliding mode control scheme is proposed to synchronize two different fractional order hyperchaotic systems in the presence of uncertainties, sector nonlinearity in the control inputs. The stability of the error dynamics is proven using Lyapunov stability theorem. Simulation results are provided to verify the feasibility and effectiveness of the proposed synchronizing method  

In this Letter, we propose a fractional-order controller to stabilize the unstable fixed points of an unstable open-loop system. Also, we show that this controller has strong ability to eliminate chaotic oscillations or reduce them to regular oscillations in the chaotic systems. This controller has simple structure and is designed very easily. To determine the control parameters, one needs only a little knowledge about the plant and therefore, the proposed controller is a suitable choice in the control of uncertain chaotic systems. © 2007 Elsevier B.V. All rights reserved  

This paper presents an algorithm for synchronizing two different chaotic systems, using a combination of the extended Kalman filter and the sliding mode controller. It is assumed that the drive chaotic system has a random excitation with a stochastically chaotic behavior. Two different cases are considered in this study. At first it is assumed that all state variables of the drive system are available, i.e. complete state measurement, and a sliding mode controller is designed for synchronization. For the second case, it is assumed that the output of the drive system does not contain the whole state variables of the drive system, and it is also affected by some random noise. By combination of... 

This paper studies and compares three nonadaptive (bidirectional, unidirectional, and sliding mode) and two adaptive (active control and backstepping) synchronization methods on the synchronizing of four pairs of identical chaotic systems (Chua's circuit, Rössler system, Lorenz system, and Lü system). Results from computer simulations are presented in order to illustrate the effectiveness of the methods and to compare them based on different criteria. © 2005 Elsevier Ltd. All rights reserved  

In this research study, chaos control of continuous time systems has been performed by using dynamic programming technique. In the first step by crossing the response orbits with a selected Poincare section and subsequently applying linear regression method, the continuous time system is converted to a discrete type. Then, by solving the Riccati equation a sub-optimal algorithm has been devised for the obtained discrete chaotic systems. In the next step, by implementing the acquired algorithm on the quantized continuous time system, the chaos has been suppressed in the Rossler and AFM systems as some case studies  

In this paper, we address global non-fragile control and synchronization of a new fractional order chaotic system. First we inspect the chaotic behavior of the fractional order system under study and also find the lowest order (2.49) for the introduced dynamics to remain chaotic. Then, a necessary and sufficient condition which can be easily extended to other fractional-order systems is proposed in terms of Linear Matrix Inequality (LMI) to check whether the candidate state feedback controller with parameter uncertainty can guarantee zero convergence of error or not. In addition, the proposed method provides a global zero attraction of error that guarantees stability around all existing... 

This paper deals with the problem of stabilizing the unstable fixed points of a class of fractional-order chaotic systems via using static output feedback. At first, a static output feedback controller designed to stabilize a fixed point of a fractional-order chaotic system is considered. Then, the maximal allowable perturbation bound around the nominal value of the output feedback gain of the designed controller, such that the stability of the intended fixed point in the closed-loop system is guaranteed, is analytically determined. Also, some numerical examples are presented to confirm the validity of the analytical results of the paper  

In this paper, based on a stability theorem proved for linear fractional-order systems, a scheme for robust synchronization of two perturbed fractional-order Chen systems is proposed. In the proposed scheme, both master and slave systems are considered to be involved with external disturbances having unknown values. It is analytically shown that any set of bounded external disturbances can be damped by the proposed method, where synchronization error will be forced and then kept inside a ball around the origin. Since during the design procedure the radius of this ball could be easily chosen by the designer, the synchronization can be done with any desired accuracy. The proposed method can be... 

This paper deals with the stability problem in LTI fractional order systems having fractional orders between 1 and 1.5. Some sufficient algebraic conditions to guarantee the BIBO stability in such systems are obtained. The obtained conditions directly depend on the coefficients of the system equations, and consequently using them is easier than the use of conditions constructed based on solving the characteristic equation of the system. Some illustrations are presented to show the applicability of the obtained conditions. For example, it is shown that these conditions may be useful in stabilization of unstable fractional order systems or in taming fractional order chaotic systems  

In this paper, a new robust finite-time hyperchaotic secure communication scheme is proposed by combining robust finite-time synchronization of two hyperchaotic systems and hyperchaotic multiplication masking technique. The mentioned synchronization is achieved by introducing new terminal sliding mode controllers. As a main novelty of the introduced scheme, an adjustable total finite time is obtained such that the decrypted message signal will be completely identical with the transmitted message signal for times larger than the discussed finite time. Compared with other secure communication schemes, the suggested method has several advantages including finite-time stability for dynamical... 

In this paper, a new approach to control continuous time chaotic systems with an unknown governing equation and limitation on the measurement of states, has been investigated. In many chaotic systems, disability to measure all of the states is a usual limitation, like in some economical, biological and many other engineering systems. Takens showed that a chaotic attractor has an astonishing feature in which it can embed to a mathematically similar attractor by using time series of one of the states. The new embedded attractor saves much information from the original attractor. This phenomenon has been deployed to present a new way to control continuous time chaotic systems, when only one of... 

In synchronization of identical chaotic systems, the control cost would be optimal in the sense that it would be zero when the synchronization is occurred. Based on this idea, in synchronization of non-identical chaotic systems, we find a signal function added to states of the derive system so that it makes the dynamics of the drive system translated into dynamics of the response system. After synchronizing two systems using this function, states of the response system will be synchronized with the equivalent states and the control cost will be optimal similar to those in the identical synchronization. © ICROS  

In this paper a nonlinear control method based on Lyapunov stability theorem is proposed to design an adaptive controller for synchronizing two different chaotic systems. It is assumed that the unknown parameters of the drive and the response chaotic systems are time varying. It is shown that the proposed scheme can identify the system parameters if the system parameters are time invariant and the richness conditions is satisfied. To demonstrate the effectiveness of the proposed technique it has been applied to Lorenz-Chen dynamic systems, as drive-response systems. Simulation results indicate that the proposed adaptive controller has a high performance in synchronizing two chaotic systems.... 

Using the Fractal Geometry in Signal processing has been extended nowadays [1]. They have found several applications in signal detection and recognitions. They use the chaotic feature of the noise and clutter and try to distinguish between the noise, clutter and the desired target [2] [3]. Recent works show that lots of clutters like sea and ground clutters have fractal behavior so this kind of approach to the signal detection has been extended these days[3][4]. In this paper we have used the Box-Counts of a signal rather than the Fractal dimension of a signal as will be defined later in the text. By applying the new defined concept we have developed different methods of signal detection. We...