Feasibility of Analog Realization of a Sliding-Mode Observer: Application to Data Transmission

One of the main contributions of this paper is to highlight the feasibility of analog realization of a chaotic observer-based communication system. The system is composed of a chaotic Colpitts oscillator considered as transmitter and a sliding-mode observer used as receiver. The method used in this realization is based on the synchronization of two chaotic systems (transmitter-receiver). Moreover, another originality of this work is the application of a sliding-mode observer to a Colpitts oscillator, which has a totally different structure with respect to it. Nevertheless, the proposed structure of the observer is designed particularly for this type of oscillator. Only one of the states of the transmitter (chosen according to theoretical criteria) is sent to the receiver which is designed to reconstruct all of the states of the transmitter knowing only the transmitted state. In order to show an application of this work, a message signal is injected into the transmitter using the so-called inclusion method. The message is then recovered by the receiver once all of the transmitter states are reconstructed. Thus, the so-called left inversion problem is resolved experimentally. The whole system (transmitter-observer) is realized using simple and standard analog components, and practical results close to simulations are obtained.

[1]  Iqbal Husain,et al.  Design and performance analysis of sliding-mode observers for sensorless operation of switched reluctance motors , 2003, IEEE Trans. Control. Syst. Technol..

[2]  S. Diop.  FROM THE GEOMETRY TO THE ALGEBRA OF NONLINEAR OBSERVABILITY , 2002 .

[3]  Latifa Boutat-Baddas,et al.  Observability Bifurcations: Application to Cryptography , 2005 .

[4]  Michael Peter Kennedy,et al.  Chaos shift keying : modulation and demodulation of a chaotic carrier using self-sychronizing chua"s circuits , 1993 .

[5]  Arthur J. Krener,et al.  Linearization by output injection and nonlinear observers , 1983 .

[6]  Driss Boutat,et al.  Sliding mode observers and observability singularity in chaotic synchronization , 2004 .

[7]  Henk Nijmeijer,et al.  An observer looks at synchronization , 1997 .

[8]  Leon O. Chua,et al.  Transmission of Digital signals by Chaotic Synchronization , 1992, Chua's Circuit.

[9]  MAO-YIN CHEN,et al.  General Synchronization of Genesio-tesi Systems , 2004, Int. J. Bifurc. Chaos.

[10]  Louis M. Pecora,et al.  Synchronizing chaotic circuits , 1991 .

[11]  Vadim I. Utkin,et al.  Sliding Modes in Control and Optimization , 1992, Communications and Control Engineering Series.

[12]  M. Fliess,et al.  Nonlinear observability, identifiability, and persistent trajectories , 1991, [1991] Proceedings of the 30th IEEE Conference on Decision and Control.

[13]  Leon O. Chua,et al.  Cryptography based on chaotic systems , 1997 .

[14]  R. Marino,et al.  Adaptive observers with arbitrary exponential rate of convergence for nonlinear systems , 1995, IEEE Trans. Autom. Control..

[15]  M. Gevers,et al.  Stable adaptive observers for nonlinear time-varying systems , 1987 .

[16]  Alain Glumineau,et al.  Commande par modes glissants d'ordre un appliquée au benchmark manutention horizontale , 2002 .

[17]  A. Sedra.  Microelectronic circuits , 1982 .

[18]  A. Krener,et al.  Nonlinear controllability and observability , 1977 .

[19]  A. Tamasevicius,et al.  Experimental demonstration of chaos from Colpitts oscillator in VHF and UHF ranges , 2004 .

[20]  A. I. Panas,et al.  Chaotic oscillators design with preassigned spectral characteristics , 2001 .

[21]  T. Başar,et al.  A New Approach to Linear Filtering and Prediction Problems , 2001 .

[22]  X. Xia,et al.  Nonlinear observer design by observer error linearization , 1989 .

[23]  Mohamed Djemai,et al.  Sliding Mode Observers , 2002 .

[24]  R. E. Kalman,et al.  New Results in Linear Filtering and Prediction Theory , 1961 .

[25]  Michael Peter Kennedy,et al.  Nonlinear analysis of the Colpitts oscillator and applications to design , 1999 .

[26]  Gregory W. Wornell,et al.  Signal processing in the context of chaotic signals , 1992, [Proceedings] ICASSP-92: 1992 IEEE International Conference on Acoustics, Speech, and Signal Processing.

[27]  Jean-Paul Gauthier,et al.  Deterministic Observation Theory and Applications: Introduction , 2001 .

[28]  Alan V. Oppenheim,et al.  Circuit implementation of synchronized chaos with applications to communications. , 1993, Physical review letters.

[29]  Alan V. Oppenheim,et al.  Synchronization of Lorenz-based chaotic circuits with applications to communications , 1993 .

[30]  J. Gauthier,et al.  A simple observer for nonlinear systems applications to bioreactors , 1992 .

[31]  J. Gauthier,et al.  Global time-varying linearization up to output injection , 1992 .