Observer Design for Semilinear Descriptor Systems with Applications to Chaos-Based Secure Communication

Gupta, Mahendra Kumar; Tomar, Nutan Kumar; Mishra, Vikas Kumar; Bhaumik, Shovan

doi:10.1007/s40819-017-0419-0

Cited by 19 publications

(13 citation statements)

References 30 publications

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“…Discussion and conclusions as well as the study's future directions are presented in Sections 5 and 6. [31] No Not needed Limited Rigid/Postulated Yes Chaotic synchronization [25,27] No Required Yes Rigid/Postulated Yes Adaptive observer [27][28][29] No Not needed Yes Rigid/Postulated No SMC observer [35] No Not needed Yes Rigid/Postulated Yes Reduced order observer [36,37] No Required Yes Rigid/Postulated No Synergetic observer [39] Yes Not needed Yes Object-defined No So, as described in Table 1 and beyond, the key advantages and main distinctive features in the design procedure of a synergetic observer in comparison with other observers are:…”

Section: Introductionmentioning

confidence: 99%

“…Finally, Moysis et al [36] explored the problem of line equilibrium chaotic system synchronization based on state observer design for a rectangular system. However, the state observers used in earlier research [27][28][29][30][31][32][33][34][35][36][37] reduce to the synergetic state observers [38][39][40] used in our work. Table 1 summarizes distinctive features of some of the explored reconstruction techniques to provide a more visible comparison between different works and approaches in the field and highlight the merit of a synergetic state observer.…”

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confidence: 99%

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A Data Secured Communication System Design Procedure with a Chaotic Carrier and Synergetic Observer

Mushenko

Dzuba²,

Nekrasov

et al. 2020

Electronics

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We have considered the problem of secure communication by means of chaotic carrier communication channels. Data protection is provided if the signal in the communication channel looks like a stochastic or noisy one, i.e., by the steganography property, and also by using advanced and secured approaches of mixing a useful signal into a chaotic carrier. The problem is to find effective and efficient techniques for useful signal reconstruction at the receiver side. We firstly use a synergetic nonlinear mathematical observer to recover the two useful signals transmitted simultaneously over a single communication channel. Compared to a known observer, the synergetic one operates with initial nonlinear models, i.e., it may be applied directly to chaotic systems. In that system structure, we consider the useful signals as unobservable variables and estimate them by the given model of a chaotic generator. A chaotic data transmission system with two channels is demonstrated; the presented mathematical procedure explains the steps of synergetic two-channel observer design. Computer simulation results prove the viability of our approach. The proposed data transmission scheme and the observer design procedure provide effective transmission and reconstruction of informational signals. Reconstruction error is up to approximately 25% but has a very short pulses shape and could be eliminated with further analog or digital filtering algorithms. As an example application, simulation of image transmission and recovery is demonstrated. The study's results may be used as a basis for further research into secure data transmission system design.Electronics 2020, 9, 497 2 of 24 Related Works and Methods OverviewThe overall issues and approaches of chaotic communications when using chaotic modulation schemes were briefly described by Riaz and Ali [21]. According to their study [21], the most common modulation schemes are: chaos shift keying (CSK); differential chaos shift keying (DCSK); additive chaos modulation (ACM); and multiplicative chaos modulation (MCM). CSK and DCKS provide secure communication by shifting between two identical or different chaotic generators. ACM and MCM provide mixing of the useful signal directly into the mathematical model of a chaotic generator in a linear (additive) or nonlinear (multiplicative) manner. In all of these schemes, one of the data secure factors is a chaotic carrier signal frequency ten times greater than the useful signal frequency or more. ACM with a combination of MCM was explored by Kevin Short in the 1990s [22] in several Electronics 2020, 9, 497 3 of 24 papers, where he proves that this kind of combined modulation does not provide security for a 3rd order system. In addition, we note that using only MCM is a more secure approach due to nonlinear mixing of the useful signal and MCM as a secure scheme is thus widely used in much research as indicated below. Different approaches and applications of chaotic data communication systems design have been illustrated in several recent papers [23][2...

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Section: Introductionmentioning

confidence: 99%

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confidence: 99%

A Data Secured Communication System Design Procedure with a Chaotic Carrier and Synergetic Observer

Mushenko

Dzuba²,

Nekrasov

et al. 2020

Electronics

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“…Over the years, chaos synchronization has found applications in many scientific disciplines, including, but not limited to, encryption and secure transmission [2][3][4][5][6][7][8], optics and lasers [9,10], engineering [11] and robotics [12][13][14]. So far, a wide variety of design approaches have been applied for synchronization [2,[15][16][17][18][19][20][21][22][23][24].…”

Section: Introductionmentioning

confidence: 99%

“…There have been several different approaches to this problem [21,[25][26][27][28][29]. This work considers the descriptor observer approach, which is studied in [15][16][17][18][19][20]28,[30][31][32]. In this work, a nonlinear system (the master system) is designed, and a desired transmitted signal is fed to the system as an input.…”

Section: Introductionmentioning

confidence: 99%

Analysis of a Chaotic System with Line Equilibrium and Its Application to Secure Communications Using a Descriptor Observer

et al. 2019

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In this work a novel chaotic system with a line equilibrium is presented. First, a dynamical analysis on the system is performed, by computing its bifurcation diagram, continuation diagram, phase portraits and Lyapunov exponents. Then, the system is applied to the problem of secure communication. We assume that the transmitted signal is an additional state. For this reason, the nonlinear system is rewritten in a rectangular descriptor form and then an observer is constructed for achieving synchronization and input reconstruction. If we assume some rank conditions (on the nonlinearities and the solvability of a linear matrix inequality (LMI)) on the system matrices then the observer synchronization can be feasible. We evaluate and demonstrate our approach with specific numerical results.

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“…Nevertheless, the theory of observer design methods for semilinear descriptor systems has been restricted to the case where nonlinear function f satisfies the bounded slope property, ie, the Lipschitz property. [4][5][6][7][8][9] In recent years, one-sided Lipschitz nonlinear systems 10 and nonlinear systems with bounded exogenous inputs 11 have also been considered for state space systems. It is observed that, apart from Lipschitz nonlinearities, monotone nonlinearities also arise in many practical situations.…”

Section: Introductionmentioning

confidence: 99%

Unknown inputs observer design for descriptor systems with monotone nonlinearities

Gupta

Tomar

Darouach

2018

Intl J Robust & Nonlinear

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Summary This paper is devoted to the reduced‐order unknown inputs observer design problem for a class of descriptor systems having generalized monotone nonlinearities. The underlying system is considered in general rectangular form with unknown inputs in dynamic and in output equations. Under some basic assumptions on system parameters, sufficient conditions for the existence of observers are proved by showing the stability of their error dynamics. The case where nonlinearity appears in output equation is also considered. The importance of the work is illustrated by real‐life and academic examples.

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Observer Design for Semilinear Descriptor Systems with Applications to Chaos-Based Secure Communication

Cited by 19 publications

References 30 publications

A Data Secured Communication System Design Procedure with a Chaotic Carrier and Synergetic Observer

A Data Secured Communication System Design Procedure with a Chaotic Carrier and Synergetic Observer

Analysis of a Chaotic System with Line Equilibrium and Its Application to Secure Communications Using a Descriptor Observer

Unknown inputs observer design for descriptor systems with monotone nonlinearities

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