Sharif Digital Repository

A modification to the control law presented in [Y. Lei, W. Xu, H. Zheng, Synchronization of two chaotic nonlinear gyros using active control, Phys. Lett. A 343 (2005) 153] is proposed. © 2007 Elsevier B.V. All rights reserved  

Multi-synchronization of chaotic systems based on the master-slave scheme as an extension of the dual synchronization problem is introduced. It is assumed that the only information available from the master systems is a linear combination of their state vectors. The design procedure for multi-synchronization through output feedback strategy is described and the sufficient condition is given. The performance of the proposed algorithm is numerically examined by applying it to the Chen-Lorenz-Rossler and the Duffing-Van der Pol chaotic systems. Simulation results show the effectiveness of the proposed scheme. © 2008 Elsevier B.V. All rights reserved  

Using the Lyapunov stability theory an adaptive control is proposed for chaos synchronization between two different systems which have stochastically time varying unknown coefficients. The stochastic variations of the coefficients about their unknown mean values are modeled through white Gaussian noise produced by the Weiner process. It is shown that using the proposed adaptive control the mean square of synchronization error converges to an arbitrarily small bound around zero. To demonstrate the effectiveness of the proposed technique, it is applied to the Lorenz-Chen and the Chen-Rossler dynamical systems, as some case studies. Simulation results indicate that the proposed adaptive... 

In this paper based on the sliding mode concept, a nonlinear delayed feedback control is proposed for stabilizing the unstable periodic orbits (UPOs) of chaotic systems. It is assumed that the period of the desired UPO is known, but its time series and the initial conditions generated the UPO are not available. The ability of the proposed control method in stabilizing the UPO of the chaotic systems is analytically proved and the effectiveness of the method is numerically examined by applying it to the chaotic Duffing system. © 2007 Elsevier Ltd. All rights reserved  

Stabilizing unstable periodic orbits of a deterministic chaotic system which is perturbed by a stochastic process is studied in this paper. The stochastic chaos is modeled by exciting a deterministic chaotic system with a white noise obtained from derivative of a Wiener process which eventually generates an Ito differential equation. It is also assumed that the chaotic system being studied has some model uncertainties which are not random. The sliding mode controller with some modifications is used for stochastic chaos suppression. It is shown that the system states converge to the desired orbit in such a way that the error covariance converges to an arbitrarily small bound around zero. As... 

Active chaos control of a tapping mode atomic force microscope (AFM) model via delayed feedback method is presented. The feedback gain is obtained and adapted according to a minimum entropy (ME) algorithm. In this method, stabilizing an unstable fixed point of the system Poincare map is achieved by minimizing the entropy of points distribution on the Poincare section. Simulation results show the feasibility of the proposed method in applying the delayed feedback technique for chaos control of an AFM system. © 2007 Elsevier B.V. All rights reserved  

In this paper a combination of Kalman filter and feedback linearization methods is used to present a controller-identifier system for synchronizing two different chaotic systems. The drive system has some unknown parameters which are supposed to have linear form within its dynamic equation. An identifier based on Kalman filter approach is designed to estimate the unknown parameters of the drive system, and simultaneously a feedback linearizing controller is used to synchronize the chaotic behavior of the response system with the drive chaotic system. The method proposed in this paper is applied to the Lure' and the Genesio dynamic systems as the drive and response chaotic systems. The... 

Chaos control of a spinning disk model via delayed feedback method is presented. The feedback gain is obtained and adapted according to a minimum entropy (ME) algorithm. In this method, stabilizing an unstable fixed point of the system Poincare map is achieved by minimizing the entropy of point distribution on the Poincare section. Simulation results show the feasibility of the proposed method in applying the delayed feedback technique for chaos control of spinning disks. © 2007 Elsevier Ltd. All rights reserved  

In this paper an indirect adaptive control algorithm is proposed to stabilize the fixed points of discrete chaotic systems. It is assumed that the functionality of the chaotic dynamics is known but the system parameters are unknown. This assumption is usually applicable to many chaotic systems, such as the Henon map, logistic and many other nonlinear maps. Using the recursive-least squares technique, the system parameters are identified and based on the feedback linearization method an adaptive controller is designed for stabilizing the fixed points, or unstable periodic orbits of the chaotic maps. The stability of the proposed scheme has been shown and the effectiveness of the control... 

In this paper the problem of synchronization between two chaotic gyros with stochastic base excitation, based on the mater-slave scheme, is studied. The stochastic excitation is modeled by applying a Gaussian white noise to the deterministic model of gyro. The white noise is derived from the Wiener process, so the resulted system is a stochastic differential equation and is modeled by an Ito differential form. Using a modified sliding mode control a Markov synchronizing control law is designed and the convergence of error states to the sliding surface in the mean square norm is analytically proved. Simulation results show the high performance of the proposed controller in stochastic chaos... 

Using the Lyapunov stability theory an adaptive control is proposed for chaos synchronization between two Chua systems which have stochastically time varying unknown coefficients. The stochastic variations of the coefficients around their unknown mean values are modeled through Gaussian white noise produced by the Wiener process. It is shown that using the proposed adaptive control the mean square of synchronization error converges to an arbitrarily small bound around zero depending on the controller feedback gain. Simulation results indicate that the proposed adaptive controller has a high performance in synchronization of chaotic Chua circuits in noisy environment. © 2007 IMACS  

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.... 

In this paper the dual synchronization of chaotic systems via output feedback strategy is investigated. The slave chaotic systems are fed by a scalar signal generated by a linear combination of the master systems state variables. The sufficient condition and design procedure for dual synchronization are presented. The proposed method is applied for dual synchronization of the Lorenz-Rossler, Rossler-Chen and Duffing-Van der Pol chaotic systems through computer simulation. The results show the effectiveness and feasibility of the proposed algorithm. © 2008 Elsevier Ltd. All rights reserved  

In this paper, the free vibration of a cantilever Timoshenko beam with a rigid tip mass is analyzed. The mass center of the attached mass need not be coincident with its attachment point to the beam. As a result, the beam can be exposed to both torsional and planar elastic bending deformations. The analysis begins with deriving the governing equations of motion of the system and the corresponding boundary conditions using Hamilton's principle. Next, the derived formulation is transformed into an equivalent dimensionless form. Then, the separation of variables method is utilized to provide the frequency equation of the system. This equation is solved numerically, and the dependency of natural... 

In this paper a variable structure system based upon sliding mode control with time varying sliding surface and variable boundary layer is introduced to synchronize two different chaotic systems with uncertain parameters. The method is applied to Lur'e-Genesio chaotic systems, as drive-response systems to investigate the effectiveness and robustness of the controlling method. In addition the simulation is repeated with a conventional sliding mode to compare the performance of the proposed sliding mode technique with a simple sliding mode control. The results show the high quality and improved performance of the method presented in the paper for synchronization of different drive-response... 

In this paper we use a combination of fuzzy clustering estimation and sliding mode method to control a chaotic system, which its mathematical model is unknown. At first the model of chaotic system is identified without using any input noise signal. In this case the recurrent property of chaotic behavior is used for estimating its model. After estimating the fuzzy model of chaos, control and on-line identification of the input-related section is applied. In this step, we estimate the system model in normal form, such that the dynamic equations can be used in sliding mode control. Finally the proposed technique is applied to the Lorenz system as an example of chaotic system. The simulation...