Observers for rectangular descriptor systems with output nonlinearities: application to secure communications and microcontroller implementation

This work considers full and reduced-order observer design for rectangular descriptor systems with application to secure communications. The output of the system is assumed to have a nonlinear term coupled with the linear part, a case that is often overlooked in the literature. The observer design is feasible under some algebraic conditions and the feasibility of a linear matrix inequality. The results are showcased through the application of secure communications, for the safe transmission and estimation of an information signal and also an encrypted image. Also, a microcontroller implementation of the master system is performed, which is the first step towards a full realisation of the design.

[1]  Christos Volos,et al.  Analysis, Synchronization and Microcontroller Implementation of a Generalized Hyperjerk System, with Application to Secure Communications Using a Descriptor Observer , 2019, 2019 Panhellenic Conference on Electronics & Telecommunications (PACET).

[2]  Shou-Wei Gao,et al.  Singular observer approach for chaotic synchronization and private communication , 2011 .

[3]  S. Bhaumik,et al.  On detectability and observer design for rectangular linear descriptor systems , 2016 .

[4]  Mahendra Kumar Gupta,et al.  Synchronization of Rossler chaotic system for secure communication via descriptor observer design approach , 2015, 2015 International Conference on Signal Processing, Computing and Control (ISPCC).

[5]  M. Rehan,et al.  Observer design for one-sided Lipschitz descriptor systems , 2016 .

[6]  Christos Volos,et al.  Passivity based control and synchronization of perturbed uncertain chaotic systems and their microcontroller implementation , 2020 .

[7]  Christos Volos,et al.  Observer design for rectangular descriptor systems with incremental quadratic constraints and nonlinear outputs—Application to secure communications , 2020, International Journal of Robust and Nonlinear Control.

[8]  G. Duan.  Analysis and Design of Descriptor Linear Systems , 2010 .

[9]  S. Strogatz.  Nonlinear Dynamics and Chaos: With Applications to Physics, Biology, Chemistry and Engineering , 1995 .

[10]  Muhammad Ali Mazidi,et al.  PIC Microcontroller , 2007 .

[11]  Junqi Yang,et al.  Synchronization for chaotic systems and chaos-based secure communications via both reduced-order and step-by-step sliding mode observers , 2013, Commun. Nonlinear Sci. Numer. Simul..

[12]  Eckehard Schöll,et al.  Handbook of Chaos Control , 2007 .

[13]  Teh-Lu Liao,et al.  An observer-based approach for chaotic synchronization with applications to secure communications , 1999 .

[14]  Junqi Yang,et al.  Singular reduced-order observer-based synchronization for uncertain chaotic systems subject to channel disturbance and chaos-based secure communication , 2014, Appl. Math. Comput..

[15]  M. Boutayeb,et al.  Generalized state-space observers for chaotic synchronization and secure communication , 2002 .

[16]  Mohamed Darouach,et al.  Unknown inputs observer design for descriptor systems with monotone nonlinearities , 2018, International Journal of Robust and Nonlinear Control.

[17]  Habib Dimassi,et al.  A new secured transmission scheme based on chaotic synchronization via smooth adaptive unknown-input observers , 2012 .

[18]  Wei Zhang,et al.  Chaotic synchronization and secure communication based on descriptor observer , 2009 .

[19]  Julien Clinton Sprott,et al.  Coexisting Hidden Attractors in a 4-D Simplified Lorenz System , 2014, Int. J. Bifurc. Chaos.

[20]  Myke Predko.  Programming and Customizing Picmicro Microcontrollers , 2000 .

[21]  Carroll,et al.  Synchronization in chaotic systems. , 1990, Physical review letters.

[22]  Christos Volos,et al.  Analysis of a Chaotic System with Line Equilibrium and Its Application to Secure Communications Using a Descriptor Observer , 2019, Technologies.

[23]  Akif Akgul,et al.  Amplitude Control Analysis of a Four-Wing Chaotic Attractor, its Electronic Circuit Designs and Microcontroller-Based Random Number Generator , 2017, J. Circuits Syst. Comput..

[24]  Leonardo Acho,et al.  A discrete-time chaotic oscillator based on the logistic map: A secure communication scheme and a simple experiment using Arduino , 2015, J. Frankl. Inst..

[25]  Wei Zhang,et al.  Exponential State Observers for Nonlinear Systems with Incremental Quadratic Constraints and Output Nonlinearities , 2018 .

[26]  Christos Volos,et al.  Analysis, Synchronization and Microcontroller Implementation of a New Quasiperiodically Forced Chaotic Oscillator with Megastability , 2019, Iranian Journal of Science and Technology, Transactions of Electrical Engineering.

[27]  Junqi Yang,et al.  Observer-Based Synchronization of Chaotic Systems Satisfying Incremental Quadratic Constraints and Its Application in Secure Communication , 2020, IEEE Transactions on Systems, Man, and Cybernetics: Systems.

[28]  S. Bhaumik,et al.  Observer Design for Semilinear Descriptor Systems with Applications to Chaos-Based Secure Communication , 2017 .

[29]  Karthikeyan Rajagopal,et al.  Modification of the Logistic Map Using Fuzzy Numbers with Application to Pseudorandom Number Generation and Image Encryption , 2020, Entropy.

[30]  Murat Arcak,et al.  Observer design for systems with multivariable monotone nonlinearities , 2003, Syst. Control. Lett..

[31]  P. Balasubramaniam,et al.  Sliding mode control design for synchronization of fractional order chaotic systems and its application to a new cryptosystem , 2017 .

[32]  Yousef Farid,et al.  Generalized projective synchronization of chaotic satellites problem using linear matrix inequality , 2014, International Journal of Dynamics and Control.

[33]  Ayub Khan,et al.  Measure of chaos and adaptive synchronization of chaotic satellite systems , 2018, International Journal of Dynamics and Control.

[34]  Sezgin Kaçar.  Analog circuit and microcontroller based RNG application of a new easy realizable 4D chaotic system , 2016 .