Effective synchronization of a class of Chua's chaotic systems using an exponential feedback coupling

In this work a robust exponential function based controller is designed to synchronize effectively a given class of Chua's chaotic systems. The stability of the drive-response systems framework is proved through the Lyapunov stability theory. Computer simulations are given to illustrate and verify the method.Comment: 12 pages, 18 figure

State estimation for coupled uncertain stochastic networks with missing measurements and time-varying delays: The discrete-time case

Copyright [2009] IEEE. This material is posted here with permission of the IEEE. Such permission of the IEEE does not in any way imply IEEE endorsement of any of Brunel University's products or services. Internal or personal use of this material is permitted. However, permission to reprint/republish this material for advertising or promotional purposes or for creating new collective works for resale or redistribution must be obtained from the IEEE by writing to [email protected]. By choosing to view this document, you agree to all provisions of the copyright laws protecting it.This paper is concerned with the problem of state estimation for a class of discrete-time coupled uncertain stochastic complex networks with missing measurements and time-varying delay. The parameter uncertainties are assumed to be norm-bounded and enter into both the network state and the network output. The stochastic Brownian motions affect not only the coupling term of the network but also the overall network dynamics. The nonlinear terms that satisfy the usual Lipschitz conditions exist in both the state and measurement equations. Through available output measurements described by a binary switching sequence that obeys a conditional probability distribution, we aim to design a state estimator to estimate the network states such that, for all admissible parameter uncertainties and time-varying delays, the dynamics of the estimation error is guaranteed to be globally exponentially stable in the mean square. By employing the Lyapunov functional method combined with the stochastic analysis approach, several delay-dependent criteria are established that ensure the existence of the desired estimator gains, and then the explicit expression of such estimator gains is characterized in terms of the solution to certain linear matrix inequalities (LMIs). Two numerical examples are exploited to illustrate the effectiveness of the proposed estimator design schemes

Finite-Time Synchronization of the Rabinovich and Rabinovich-Fabrikant Chaotic Systems for Different Evolvable Parameters

This paper addresses the challenge of synchronizing the dynamics of two distinct 3D chaotic systems, specifically the Rabinovich and Rabinovich-Fabrikant systems, employing a finite-time synchronization approach. These chaotic systems exhibit diverse characteristics and evolving chaotic attractors, influenced by specific parameters and initial conditions. Our proposed low-cost finite-time synchronization method leverages the signum function's tracking properties to facilitate controlled coupling within a finite time frame. The design of finite-time control laws is rooted in Lyapunov stability criteria and lemmas. Numerical experiments conducted within the MATLAB simulation environment demonstrate the successful asymptotic synchronization of the master and slave systems within finite time. To assess the global robustness of our control scheme, we applied it across various system parameters and initial conditions. Remarkably, our results reveal consistent synchronization times and dynamics across these different scenarios. In summary, this study presents a finite-time synchronization solution for non-identical 3D chaotic systems, showcasing the potential for robust and reliable synchronization under varying conditions

Robust adaptive synchronization of a class of uncertain chaotic systems with unknown time-delay

In this paper, a robust adaptive control strategy is proposed to synchronize a class of uncertain chaotic systems with unknown time delays. Using Lyapunov theory and Lipschitz conditions in chaotic systems, the necessary adaptation rules for estimating uncertain parameters and unknown time delays are determined. Based on the proposed adaptation rules, an adaptive controller is recommended for the robust synchronization of the aforementioned uncertain systems that prove the robust stability of the proposed control mechanism utilizing the Lyapunov theorem. Finally, to evaluate the proposed robust and adaptive control mechanism, the synchronization of two Jerk chaotic systems with finite non-linear uncertainty and external disturbances as well as unknown fixed and variable time delays are simulated. The simulation results confirm the ability of the proposed control mechanism in robust synchronization of the uncertain chaotic systems as well as to estimate uncertain and unknown parameters

Robust synchronization of fractional-order unified chaotic systems via linear control

AbstractA new scheme for accomplishing synchronization between two fractional-order unified chaotic systems is proposed in this paper. The scheme does not require that the nonlinear dynamics of the synchronization error system must be eliminated. Moreover, the parameter of the systems does not have to be known. A controller is a linear feedback controller, which is simple in implementation. It is designed based on an LMI condition. The LMI condition guarantees that the synchronization between the slave system and the master system is achieved. Numerical simulations are performed to demonstrate the effectiveness of the proposed scheme

Predefined-time synchronization of 5D Hindmarsh–Rose neuron networks via backstepping design and application in secure communication

In this paper, the fast synchronization problem of 5D Hindmarsh–Rose neuron networks is studied. Firstly, the global predefined-time stability of a class of nonlinear dynamical systems is investigated under the complete beta function. Then an active controller via backstepping design is proposed to achieve predefined-time synchronization of two 5D Hindmarsh–Rose neuron networks in which the synchronization time of each state variable of the master-slave 5D Hindmarsh–Rose neuron networks is different and can be defined in advance, respectively. To show the applicability of the obtained theoretical results, the designed predefined-time backstepping controller is applied to secure communication to realize asynchronous communication of multiple different messages. Three numerical simulations are provided to validate the theoretical results