Search

In a master slave configuration of strictly different commensurate fractional order Liouvillian systems, the generalized synchronization problem of multiple decoupled families of Liouvillian systems is addressed. The main key ingredient is to find canonical forms for the original systems, from a family of fractional differential primitive elements based on output of each system, taking into account the Liouvillian feature. Fractional order dynamical controllers are designed to solve the generalized multi-synchronization problem. Moreover, it is shown that adding diffusive coupling terms in the dynamical controllers solves the synchronization problem with complex interaction between slave systems, with any type of interplay. Finally, some numerical examples show the effectiveness of the proposed approach. [ABSTRACT FROM AUTHOR]

In this article we propose the use of a Liouvillian chaotic system on a master–slave scheme for secure communications. Two forms of data encryption are presented, the first is a state observer based on the Super-Twisting algorithm, the second is a receiver designed through the properties of Liouvillian systems, this last receiver does not suffer from data loss due to synchronization error present on state observer based encryption. To test the advantages of this encryption, images and text will be used as transmitted data. [ABSTRACT FROM AUTHOR]

Abstract: In this paper we deal with the synchronization and parameter estimations of an uncertain Rikitake system and its application in secure communications employing chaotic parameter modulation. The strategy consists of proposing a receiver system which tends to follow asymptotically the unknown Rikitake system, refereed as transmitter system. The gains of the receiver system are adjusted continually according to a convenient high order sliding-mode adaptative controller (HOSMAC), until the measurable output errors converge to zero. By using HOSMAC, synchronization between transmitter and receiver is achieved and message signals are recovered. The convergence analysis is carried out by using Barbalat’s Lemma. [Copyright &y& Elsevier]

Abstract: Chaotic systems synchronization and anti-synchronization problems are tackled by means of differential and algebraic techniques for nonlinear systems. An algebraic observer is proposed for systems satisfying an algebraic observability condition. This observer can be used as a slave system whose states are synchronized with the master (chaotic) system. This approach has the advantages of being independent of the chaotic nature of the master system, it uses a reduced set of measurable signal from the master system and it also solves the anti-synchronization problem as a straightforward extension of the synchronization one. A Colpitts oscillator is given to illustrate the effectiveness of the suggested approach. [Copyright &y& Elsevier]

Abstract: The aim of this paper is the synthesis of a robust control law for chaos suppression of a class of non-linear oscillator with affine control input. A robust state observer based active controller, which provides robustness against model uncertainties and noisy output measurements is proposed. The closed-loop stability for the underlying closed-loop system is done via the regulation and estimation errors dynamics. The performance of the proposed control law is illustrated with numerical simulations. The method is general and can be applied to various non-linear systems which satisfy the conditions required. [Copyright &y& Elsevier]