Moez Feki

An adaptive chaos synchronization scheme applied to secure communication

Abstract This paper deals with the problem of synchronization of a class of continuous-time chaotic systems using the drive-response concept. An adaptive observer-based response system is designed to synchronize with a given chaotic drive system whose dynamical model is subjected to unknown parameters. Using the Lyapunov stability theory an adaptation law is derived to estimate the unknown parameters. We show that synchronization is achieved asymptotically. The approach is next applied to chaos-based secure communication. To demonstrate the efficiency of the proposed scheme numerical simulations are presented.

An adaptive feedback control of linearizable chaotic systems

This paper proposes an adaptive feedback controller for a class of chaotic systems. This controller can be used for tracking a smooth orbit that can be a limit cycle or a chaotic orbit of another system. Based on Lyapunov approach, the adaptation law is determined to tune the controller gain vector in order to track a predetermined linearizing feedback control. To demonstrate the efficiency of the proposed scheme, two well-known chaotic systems namely Chuas circuit and a Lure-like system are considered as illustrative examples. 2002 Elsevier Science Ltd. All rights reserved.

Observer-based exact synchronization of ideal and mismatched chaotic systems

Abstract In this Letter, an observer-based chaotic synchronization scheme is proposed. Our method concerns chaotic systems having special triangular form. Using the sliding mode theory, the synchronization of the response system with the drive system is achieved in finite time. An application to secure chaotic communication is also proposed. To demonstrate the efficiency of the proposed scheme, two well-known chaotic systems: Lure-like system and Duffing equation are considered as illustrative examples.

Secure digital communication using discrete-time chaos synchronization

Abstract In this paper we propose some secure digital communication schemes using discrete chaotic systems. In our approach a message is encrypted at the transmitter using chaotic modulation. Next, the driving signal synchronizes the receiver using discrete observer design or drive-response concept. Finally, by reverting the coding procedure the transmitted message is reconstructed. To demonstrate the efficiency of our communication schemes a modified Henon’s map is considered as an illustrative example.

A chaotic masking scheme by using synchronized chaotic systems

Abstract We present a new chaotic masking scheme by using synchronized chaotic systems. In this method, synchronization and message transmission phases are separated, and while synchronization is achieved in the synchronization phases, the message is only sent in message transmission phases. We show that if synchronization is achieved exponentially fast, then under certain conditions any message of any length could be transmitted and successfully recovered provided that the synchronization length is sufficiently long. We also show that the proposed scheme is robust with respect to noise and parameter mismatch under some mild conditions.

Observer-based chaotic synchronization in the presence of unknown inputs

This paper deals with the problem of synchronization of chaotic dynamical systems. We consider a drive-response type of synchronization via a scalar transmitted signal. Unlike most works we consider the presence of some unknown inputs in the drive system and that no knowledge about their nature is available. A reduced-order observer-based response system is designed to synchronize with the missing states. We show that under some assumptions the synchronization is exponentially achieved. The efficiency of our method is confirmed by numerical simulations of two wellknown chaotic systems: Chuas circuit and Lure system. 2002 Elsevier Science Ltd. All rights reserved.

CONTROL OF A PWM INVERTER USING PROPORTIONAL PLUS EXTENDED TIME-DELAYED FEEDBACK

Pulse width modulation (PWM) current-mode single phase inverters are known to exhibit bifurcations and chaos when parameters vary or if the gain of the proportional controller is arbitrarily increa...

Adaptive time-delayed feedback for chaos control in a PWM single phase inverter

Many power converters exhibit chaotic behaviors and bifurcations when conventional feedback corrector are badly tuned or when parameters vary. Time-Delayed Feedback Control (TDFC) can be used to stabilize them using a state feedback delayed by the period of the unstable orbit (UPO) to be stabilized. An obvious advantage of this method is the robustness because it does not require the knowledge of an accurate model but only the period of the target UPO. In this paper, TDFC is applied to a PWM current-programmed single phase inverter concurrently with a proportional corrector in order to avoid bifurcations and chaos and to stabilize the fundamental UPO over a widened range of application. Moreover an improvement of the dynamical performances is realized by defining an adaptive law for the TDFC.

MODEL-INDEPENDENT ADAPTIVE CONTROL OF CHUA'S SYSTEM WITH CUBIC NONLINEARITY

This paper proposes a linear adaptive state feedback controller which achieves asymptotic tracking of the controlled cubic Chua’s system. The gain vector is tuned using an adaptation law derived using the Lyapunov stability theory. The aim is to design an adaptive controller that mimics a predetermined input{output linearizing controller known for its eectiv e performance in output tracking. We show that the system model is not necessary to construct the controller. We also show that synchronization of two cubic Chua’s systems can be achieved. Numerical simulations are presented to illustrate the eciency of the proposed scheme.

SYNCHRONIZATION OF CHAOTIC SYSTEMS WITH PARAMETRIC UNCERTAINTIES USING SLIDING OBSERVERS

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.