Adaptive observers for robust synchronization of chaotic systems (original) (raw)

Adaptive Observers With Persistency of Excitation for Synchronization of Chaotic Systems

IEEE Transactions on Circuits and Systems I: Regular Papers, 2000

We address the problem of master-slave synchronization of chaotic systems under parameter uncertainty and with partial measurements. Our approach is based on observer-design theory hence, we view the master dynamics as a system of differential equations with a state and a measurable output and we design an observer (tantamount to the slave system) which reconstructs the dynamic behavior of the master. The main technical condition that we impose is persistency of excitation (PE), a property well studied in the adaptive control literature. In the case of unknown parameters and partial measurements we show that synchronization is achievable in a practical sense, that is, with "small" error. We also illustrate our methods on particular examples of chaotic oscillators such as the Lorenz and the Lü oscillators. Theoretical proofs are provided based on recent results on stability theory for time-varying systems.

Observer based synchronization of chaotic systems

Physical Review E, 1996

We show that the synchronization of chaotic systems can be achieved by using the observer design techniques which are widely used in the control of dynamical systems. We show that local synchronization is possible under relatively mild conditions and global synchronization is possible if the chaotic system can be transformed into a special form. We also give some examples including the Lorenz, the Rössler systems, and Chua's oscillator which are known to exhibit chaotic behavior, and show that in these systems synchronization by using observers is possible.

Synchronization of a class of chaotic signals via robust observer design

Chaos, Solitons & Fractals, 2008

In this paper the signal synchronization of a class of chaotic systems based on robust observer design is tackled. The task is the synchronization of the signals generated by two Chen oscillators with different initial condition. The proposed observer is robust against model uncertainties and noisy output measurements. An alternative system representation is proposed to transform the measured disturbance onto system disturbance, which leads a more adequate observer structure. The proposed methodology contains an uncertainty estimator based on the predictive contribution to infer the unobservable uncertainties and corrective contribution to estimate the observable uncertainties; which provides robustness against noisy measurements and model uncertainties. Convergence analysis of the proposed estimation methodology is realized, analyzing the dynamic equation of the estimation error, where asymptotic convergence is shown. Numerical experiments illustrate the good performance of the proposed methodology.

Adaptive Observer-Based Synchronisation of Chaotic Systems in Presence of Information Constraints

IFAC Proceedings Volumes, 2006

We analyze performance of adaptive chaotic synchronisation system under information constraints in assumption that some system parameters are unknown and only system output is measured. Such a problem was studied previously in absence of information constraints based on adaptive observer scheme, allowing for its usage for message transmission systems. We provide analytical bounds for the closed-loop system performance (asymptotic error) and conduct a numerical case study for a typical chaotic system, namely the Chua circuit, in presence of information constraints. It is shown that the timevarying quantiser with one-step memory provides reasonable approximation for the minimum transmission rate for adaptive state estimation.

A New Approach for the Observer-Based Synchronization of Chaotic Systems

IFAC Proceedings Volumes, 2005

In this paper, a new framework for the synchronization of chaotic systems is presented. The synchronization problem of a large class of chaotic systems is formulated as an observer synthesis problem for an appropriate class of linear parameter-varying (LPV) systems. The result introduced in this paper shows that LPV techniques can successfully be used in the context of chaotic systems synchronization. Two examples are considered in order to show the applicability of the LPV approach.

A stable adaptive synchronization scheme for uncertain chaotic systems via observer

Chaos, Solitons & Fractals, 2009

ABSTRACT A novel observer-based adaptive synchronization scheme is presented which is used in a chaos communication system. Also, a new nonlinear stochastic adaptive sliding mode observer is extended to reconstruct the states of the stochastic chaotic transmitter at the receiver. The observer is able to overcome the effect of model and parameters uncertainties as well as transmitter, channel and measurement noises. Moreover, a theorem is presented to prove the stability in probability of the proposed observer using stochastic Lyapunov stability criterion. The time-varying adaptation gains of the observer resulted from the proposed theorem ensure fast convergence of the estimated states. Adaptation gains are bounded and do not have any singularity problem especially when the mean value of the observer states’ error. In this paper, the parameters of the transmitter are unknown or are changed intermittently to increase the security of the message transmission. Performance of the message reconstruction in the receiver is enhanced using the scalar transmitted signal to estimate the parameters of the transmitter.

Observer-based synchronization scheme for a class of chaotic systems using contraction theory

Nonlinear Dynamics, 2011

In this paper, an adaptive synchronization scheme is proposed for a class of nonlinear systems. The design utilizes an adaptive observer, which is quite useful in establishing a transmitter-receiver kind of synchronization scheme. The proposed approach is based on contraction theory and provides a very simple way of establishing exponential convergence of observer states to actual system states. The class of systems addressed here has uncertain parameters, associated with the part of system dynamics that is a function of measurable output only. The explicit conditions for the stability of the observer are derived in terms of gain selection of the observer. Initially, the case without uncertainty is considered and then the results are extended to the case with uncertainty in parameters of the system. An application of the proposed approach is presented to synchronize the family of N chaotic systems which are coupled through the output variable only. The numerical results are presented for designing an adaptive observer for the chaotic Chua system to verify the efficacy of the proposed approach. Explicit bounds on observer gains are derived by exploiting the properties of the chaotic attractor exhibited by Chua's system. Convergence of uncertain parameters is also analyzed for this case and numerical simulations depict the convergence of parameter estimates to their true value.

SYNCHRONIZATION OF CHAOTIC SYSTEMS WITH PARAMETRIC UNCERTAINTIES USING SLIDING OBSERVERS

International Journal of Bifurcation and Chaos, 2004

This paper is concerned with synchronization of chaotic systems. We consider a drive-response type of synchronization via a scalar transmitted signal. Given some structural conditions of chaotic systems, a sliding observer-based response system is constructed to synchronize with the drive system within a finite time. Moreover, if the observer gain is judiciously chosen, robustness with respect to bounded parameter variations is guaranteed. To improve furthermore the performance of the response system, unknown parameters are adaptively estimated in conjunction with the sliding observer. To demonstrate the efficiency of the proposed approach numerical simulation results are presented.

Synchronization of Chaotic Systems: A Generic Nonlinear Integrated Observer-Based Approach

Complexity, 2021

The purpose of this research is to study the synchronization of two integrated nonlinear systems with time delay and disturbances. A nonlinear system is a system in which the difference in output is not relative to the difference in input. A new control methodology for synchronization of the two chaotic systems master and slave is recognized by means of the unique integrated chaotic synchronous observer and the integrated chaotic adaptive synchronous observer. The instantaneous approximation states of the master and slave systems are accomplished by means of methods for suggesting observers for every one of the master and slave systems and by the production of error signals between these approximated states. This approximated synchronization error signal and state approximation errors meet at the origin by means of methods involving a particular observer-based feedback control signal to ensure synchronization and state approximation. Using Lyapunov stability theory, adaptive and non...