Synchronization Of Nonlinear Dynamical Systems Research Articles

Lag synchronization of nonlinear dynamical systems via asymmetric saturated impulsive control

In this paper, an asymmetric saturated impulsive control scheme is put forward and is suggested to realize the lag synchronization of two coupled dynamical systems in the master-slave pattern. We analyze the stability and then estimate the domain of attraction of the error system between slave system and master system based on Lyapunov stability theory, sector nonlinearity model approach, matrix inequality, set invariance, Schur complement. In addition, some sufficient conditions are also given for the lag synchronization of two nonlinear dynamical systems under this impulsive control scheme without actuator saturation. Finally, simulation results for a new chaotic oscillator and a Hopfield-type dynamic neural network are presented to show the feasibility and effectiveness of the obtained results.

Chaos synchronization of nonlinear dynamical systems via a novel analytical approach

This paper deals with the synchronization between two non-identical 4-D hyperchaotic systems. The nonlinear control technique is used for synchronization. The stability analysis of the error dynamics system is done by (i) Lyapunov's second method and (ii) Cardano's method. Four different expressions of the controller are presented in the paper and a comparison between the two methods are given. We notice that the Cardano's method is better than the Lyapunov approach. Finally, theoretical and numerical simulations are given to illustrate and verify the results.

Parameter identification and adaptive impulsive synchronization of uncertain complex-variable chaotic systems

Synchronization of nonlinear dynamical systems with complex variables has attracted much more attention in various fields of science and engineering. In this paper, the problem of parameter identification and adaptive impulsive synchronization for a class of chaotic (hyperchaotic) complex nonlinear systems with uncertain parameters is investigated. Based on the theories of adaptive control and impulsive control, a synchronization scheme is designed to make a class of chaotic and hyperchaotic complex systems asymptotically synchronized, and uncertain parameters are identified simultaneously in the process of synchronization. Particularly, the proposed adaptive–impulsive control laws for synchronization are simple and can be readily applied in practical applications. The synchronization of two identical chaotic complex Chen systems and two identical hyperchaotic complex Lu systems are taken as two examples to verify the feasibility and effectiveness of the proposed controllers and identifiers.

Improvements and applications of entrainment control for nonlinear dynamical systems

This paper improves the existing entrainment control approaches and develops unified schemes to chaos control and generalized (lag, anticipated, and complete) synchronization of nonlinear dynamical systems. By introducing impulsive effects to the open-loop control method, we completely remove its restrictions on goal dynamics and initial conditions, and derive a sufficient condition to estimate the upper bound of impulsive intervals to ensure the global asymptotic stability. We then propose two effective ways to implement the entrainment strategy which combine open-loop and closed-loop control, and we prove that the feedback gains can be chosen according to a lower bound or be tuned with an adaptive control law. Numerical examples are given to verify the theoretical results and to illustrate their applications.

NONLINEAR DYNAMICAL SYSTEM AND CHAOS SYNCHRONIZATION

Chaos synchronization of nonlinear dynamical systems has been studied through theoretical and numerical techniques. For the synchronization of two identical nonlinear chaotic dynamical systems a theorem has been constructed based on the Lyapunov function, which requires a minimal knowledge of system's structure to synchronize with an identical response system. Numerical illustrations have been provided to verify the theorem.

State and parameter estimation in nonlinear systems as an optimal tracking problem

In verifying and validating models of nonlinear processes it is important to incorporate information from observations in an efficient manner. Using the idea of synchronization of nonlinear dynamical systems, we present a framework for connecting a data signal with a model in a way that minimizes the required coupling yet allows the estimation of unknown parameters in the model. The need to evaluate unknown parameters in models of nonlinear physical, biophysical, and engineering systems occurs throughout the development of phenomenological or reduced models of dynamics. Our approach builds on existing work that uses synchronization as a tool for parameter estimation. We address some of the critical issues in that work and provide a practical framework for finding an accurate solution. In particular, we show the equivalence of this problem to that of tracking within an optimal control framework. This equivalence allows the application of powerful numerical methods that provide robust practical tools for model development and validation.

Impulsive Control and Synchronization of Nonlinear Dynamical Systems and Application to Secure Communication

Impulsive control is a newly developed control theory which is based on the theory of impulsive differential equations. In this paper, we stabilize nonlinear dynamical systems using impulsive control. Based on the theory of impulsive differential equations, we present several theorems on the stability of impulsive control systems. An estimation of the upper bound of the impulse interval is given for the purpose of asymptotically controlling the nonlinear dynamical system to the origin by using impulsive control laws. In this paper, impulsive synchronization of two nonlinear dynamical systems is reformulated as impulsive control of the synchronization error system. We then present a theorem on the asymptotic synchronization of two nonlinear systems by using synchronization impulses. The robustness of impulsive synchronization to additive channel noise and parameter mismatch is also studied. We conclude that impulsive synchronization is more robust than continuous synchronization. Combining both conventional cryptographic method and impulsive synchronization of chaotic systems, we propose a new chaotic communication scheme. Computer simulation results based on Chua's oscillators are given.