Finite-time structure identification and synchronization of drive-response systems with uncertain parameter

This paper proposes an approach of finite-time synchronization to identify the topological structure and unknown parameters simultaneously for under general complex dynamical networks. Based on the finite-time stability theory, an effective control input and a feedback control with an updated law are designed to realize finite-time synchronization between two complex networks. The unknown network topological structure and system parameters of uncertain general complex dynamical networks are identified simultaneously. Since finite-time topology identification means the suboptimum in identified time, the results of this paper are important. Several useful criteria for finite-time synchronization are given. Finally, two examples simulations for supporting the theoretical results are also provided.     

Chaos and chaos synchronization for a non-autonomous rotational machine systems

Chaos and chaos synchronization of the centrifugal flywheel governor system are studied in this paper. By mechanics analyzing, the dynamical equation of the centrifugal flywheel governor system is established. Because of the non-linear terms of the system, the system exhibits both regular and chaotic motions. The characteristic of chaotic attractors of the system is presented by the phase portraits and power spectra. The evolution from Hopf bifurcation to chaos is shown by the bifurcation diagrams and a series of Poincaré sections under different sets of system parameters, and the bifurcation diagrams are verified by the related Lyapunov exponent spectra. This letter addresses control for the chaos synchronization of feedback control laws in two coupled non-autonomous chaotic systems with three different coupling terms, which is demonstrated and verified by Lyapunov exponent spectra and phase portraits. Finally, numerical simulations are presented to show the effectiveness of the proposed chaos synchronization scheme.     

Chaos synchronization between two different chaotic dynamical systems

This work presents chaos synchronization between two different chaotic systems by nonlinear control laws. First, synchronization problem between Genesio system and Rossler system has been investigated, and then the similar approach is applied to the synchronization problem between Genesio system and a new chaotic system developed recently in the literature. The control performances are verified by two numerical examples.     

Chaos synchronization between two different fractional-order hyperchaotic systems

This work investigates chaos synchronization between two different fractional-order hyperchaotic system (FOHS)s. A novel FOHS is also proposed in this paper. The Chen FOHS is controlled to be a new FOHS and the Lü FOHS, respectively. The analytical conditions for the synchronization of these pairs of different FOHSs are derived by utilizing Laplace transform. Furthermore, synchronization between two different FOHSs is achieved by utilizing feedback control method in a quite short period and both remain in chaotic states. Numerical simulations are used to verify the theoretical analysis using different values of the fractional-order parameter.     

超混沌系统的函数投影同步与参数辨识

研究了一参数未知超混沌系统的函数投影同步问题．基于李雅谱诺夫稳定性理论,设计了实现混沌系统函数投影同步的有效非线性控制器,可以快速实现超混沌系统的加速函数投影同步,同时设计了参数控制律,有效的辨识了系统的未知参数,数值仿真验证了理论分析和数值计算的正确性．     

Lag synchronization of chaotic systems with parameter mismatches

The paper studies the effect of parameter mismatch on lag synchronization of chaotic systems. It shall be shown that lag synchronization of coupled systems may weakly achieve, when parameter mismatch is small. The error bound of lag synchronization arising from the parameter mismatch is also estimated by rigorously theoretical analysis. Numerical simulations on Chua oscillator are presented to verify the theoretical results.     

Chaos synchronization between two different chaotic systems using active control

This work presents chaos synchronization between two different chaotic systems by using active control. This technique is applied to achieve chaos synchronization for each pair of the dynamical systems Lorenz, Lü and Chen. Numerical simulations are shown to verify the results.     

Parameter identification and synchronization of fractional-order chaotic systems

The knowledge about parameters and order is very important for synchronization of fractional-order chaotic systems. In this article, identification of parameters and order of fractional-order chaotic systems is converted to an optimization problem. Particle swarm optimization algorithm is used to solve this optimization problem. Based on the above parameter identification, synchronization of the fractional-order Lorenz, Chen and a novel system (commensurate or incommensurate order) is derived using active control method. The new fractional-order chaotic system has four-scroll chaotic attractors. The existence and uniqueness of solutions for the new fractional-order system are also investigated theoretically. Simulation results signify the performance of the work.     

Chaos synchronization of resistively coupled Duffing systems: Numerical and experimental investigations

This paper studies chaos synchronization dynamics of two resistively coupled Duffing systems, through numerical and experimental investigations. Various bifurcation structures are derived and it is found that chaos appear suddenly, through period doubling cascades. The experimental study of these systems is carried out with appropriate software electronic circuit, proposed using the BSIMV3.3 parameters for the investigation of the dynamical behavior. The appropriate coupled coefficient for chaos synchronization is found using numerical and experimental simulations. The reliability of the analytical formulas is approved by the good agreement with the results obtained by both numerical and experiment simulations.     

Chaos synchronization between two novel different hyperchaotic systems with unknown parameters

This work is devoted to investigating the synchronization between two novel different hyperchaotic systems with fully unknown parameters, i.e., an uncertain hyperchaotic Lorenz system and an uncertain hyperchaotic Lü system. Based on the Lyapunov stability theory, a new adaptive controller with parameter update law is designed to synchronize these two hyperchaotic systems asymptotically and globally. Numerical simulations are presented to verify the effectiveness of the synchronization scheme.     

Chaos synchronization between two different chaotic systems via nonlinear feedback control

This work presents chaos synchronization between two different chaotic systems via nonlinear feedback control. On the basis of a converse Lyapunov theorem and balanced gain scheme, control gains of controller are derived to achieve chaos synchronization for the unified chaotic systems. Numerical simulations are shown to verify the results.     

Gradient based iterative parameter identification for Wiener nonlinear systems

This paper focuses on the identification problem of Wiener nonlinear output error systems. The application of the key-term decomposition technique provides a special form of the Wiener model with polynomials, where all the model parameters to be estimated are separated. To solve the identification problem of Wiener nonlinear output error systems with the unmeasurable variables in the information vector, an auxiliary model-based gradient iterative algorithm is presented by replacing the unmeasurable variables with their corresponding iterative estimates. The performances of the proposed algorithm are analyzed and compared by using numerical examples.     

Dynamical level set method for parameter identification of nonlinear parabolic distributed parameter systems

This article considers a dynamical level set method for the identification problem of the nonlinear parabolic distributed parameter system, which is based on the solvability and stability of the direct PDE (partial differential equation) in Sobolev space. The dynamical level set algorithms have been developed for ill-posed problems in Hilbert space. This method can be regarded as a asymptotical regularization method as long as a certain stopping rule is satisfied. Hence, the convergence analysis of the method is established similar to the proof of convergence of asymptotical regularization. The level set converges to a solution as the artificial time evolves to infinity. Furthermore, the proposed level set method is proved to be stable by using Lyapunov stability theorem, which is constructed in my previous article.Numerical tests are discussed to demonstrate the efficacy of the dynamical level set method, which consequently confirm the level set method to be a powerful tool for the identification of the parameter.     

Chaos control and function projective synchronization of fractional-order systems through the backstepping method

We study the chaos control and the function projective synchronization of a fractional-order T-system and Lorenz chaotic system using the backstepping method. Based on stability theory, we consider the condition for the local stability of nonlinear three-dimensional commensurate fractional-order system. Using the feedback control method, we control the chaos in the considered fractional-order T-system. We simulate the function projective synchronization between the fractional-order T-system and Lorenz system numerically using MATLAB and depict the results with plots.     

A stability result for distributed parameter identification in bilinear systems

In this paper we give a stability result for the problem of identifying distributed parameters (for instance, a conductivity matrix) in partial differential equations. The result is used to establish an error estimate for an algorithm to identify the parameter.     

Chaos synchronization for master slave piecewise linear systems: Application to Chua’s circuit

This paper deals with chaos synchronization for master slave piecewise linear systems. The synchronization problem is formulated as a global stability problem of error synchronization dynamics. New sufficient conditions are provided using a Lyapunov approach and the so-called S-procedure. We show that the synchronization problem can be solved as an optimization problem subject to a set of Linear Matrix Inequalities (LMI) for which a state feedback controller is designed efficiently. The effectiveness of the proposed solution is verified via simulation results using the original Chua’s circuit model. Furthermore, it will be proven that the new sufficient conditions relaxed the conservatism of previous existing works.     

Lag and anticipatory synchronization based parameter estimation scheme in modulated time-delayed systems

In this article, we have shown that using delay dynamical systems as base, one can use the modulation of the various parameters, to transmit multiple signals through a single chaotic time series. It is shown that under certain conditions the original signals and parameters of the driving signals can be recovered with the help of an adaptive demodulator. An important aspect of the present method is that the communication is possible between two time-delayed systems with parameter mismatch using lag and anticipatory synchronization. The whole idea is presented on the basis of Mackey–Glass system, with variable time delay.     

Stochastic gradient with changing forgetting factor-based parameter identification for Wiener systems

The parameter estimation problem is considered for a class Wiener systems. First, the effect of the forgetting factor on the stochastic gradient algorithm is analyzed. Then, a Wiener system stochastic gradient with a changing forgetting factor algorithm is presented which makes full use of the forgetting factor. Finally, an example is provided to test and verify the effectiveness of the proposed algorithms.     

Chaos synchronization of nonlinear Bloch equations

In this paper, the problem of chaos synchronization of Bloch equations is considered. A novel nonlinear controller is designed based on the Lyapunov stability theory. The proposed controller ensures that the states of the controlled chaotic slave system asymptotically synchronizes the states of the master system. A numerical example is given to illuminate the design procedure and advantage of the result derived.     

Chaos synchronization using fuzzy logic controller

The design of a rule-based controller for a class of master-slave chaos synchronization is presented in this paper. In traditional fuzzy logic control (FLC) design, it takes a long time to obtain the membership functions and rule base by trial-and-error tuning. To cope with this problem, we directly construct the fuzzy rules subject to a common Lyapunov function such that the master–slave chaos systems satisfy stability in the Lyapunov sense. Unlike conventional approaches, the resulting control law has less maximum magnitude of the instantaneous control command and it can reduce the actuator saturation phenomenon in real physic system. Two examples of Duffing–Holmes system and Lorenz system are presented to illustrate the effectiveness of the proposed controller.