An algebraic state estimation approach for the recovery of chaotically encrypted messages

In this article we use a variant of recently introduced algebraic state estimation method obtained from a fast output signal time derivatives computation process. The fast time derivatives calculations are entirely based on the consequences of using the "algebraic approach" in linear system description. Here we demonstrate, through computer simulations, the effectiveness of the proposed algebraic approach in the accurate and fast (i.e. non asymptotic) estimation of the chaotic states in some of the most popular chaotic systems. The propsed state estimation method can then be used in a coding-decoding process of a secret message transmission using the message modulated chaotic system states and the reliable transmission of the chaotic system output. Simulation examples, using Chen's chaotic system output and the Rossler system, demonstrate the importance of the proposed fast state estimation method in the accurate extraction of a chaotically encrypted message. In our simulation results, the proposed approach is shown to be quite robust with respect to (computer generated) transmission noise perturbations. We also propose a way to evade computational singularities associated with the local lack of observability of certain chaotic system outputs and still carry out the encrypting and decoding of secret messages in a reliable manner

Non-linear estimation is easy

Non-linear state estimation and some related topics, like parametric estimation, fault diagnosis, and perturbation attenuation, are tackled here via a new methodology in numerical differentiation. The corresponding basic system theoretic definitions and properties are presented within the framework of differential algebra, which permits to handle system variables and their derivatives of any order. Several academic examples and their computer simulations, with on-line estimations, are illustrating our viewpoint

Towards a model-free output tracking of switched nonlinear systems

We extend previous works on model-free control to switched nonlinear SISO systems. Our contribution, which is utilizing new algebraic methods for numerical differentiations, yields PID-like regulators which ensure practical stability. Several academic examples, with convincing computer simulations, are illustrating our approach

Algebraic observer for a class of switched systems with Zeno phenomenon

International audienceFor a large class of switched systems with zeno phenomenon, classical observer cannot be applied directly since the terms leading to zeno phenomenon are not derivable. However in this paper, by assuming that these terms are integrable in the less restrictive way, we can define a new output, with which algebraic observer can then be adopted to estimate the states of the studied switched systems with zeno phenomenon. For simplicity, the main idea is explained via normal forms, while it can also be extended to generic switched systems

Finite time observers: application to secure communication

International audienceIn this paper, control theory is used to formalize finite time chaos synchronization as a nonlinear finite time observer design issue. This paper introduces a finite time observer for nonlinear systems that can be put into a linear canonical form up to output injection. The finite time convergence relies on the homogeneity properties of nonlinear systems. The observer is then applied to the problem of secure data transmission based on finite time chaos synchronization and the two-channel transmission method

Differentiator application in altitude control for an indoor blimp robot

International audienceThis paper presents design of altitude controller with disturbance compensation for an indoor blimp robot and its realisation. Due to hardware restrictions, the altitude control behaviour of blimp is modelled as a switched system with a constant time-delay complemented with uncertain bounded disturbances. In order to achieve state estimation, four differentiators are applied and compared, then HOMD (homo-geneous finite-time) differentiator is chosen as an observer for vertical velocity and switching signal estimation. Next, a predictor-based controller is conceived, and in order to compensate the perturbation, the method for disturbance evaluation is designed still with the help of HOMD differentiator. Control scheme is implemented by Matlab Simulink, and finally, the performance of blimp altitude controller is verified in experiments

Design and Implementation of Secure Chaotic Communication Systems

Chaotic systems have properties such as ergodicity, sensitivity to initial conditions/parameter mismatches, mixing property, deterministic dynamics, structure complexity, to mention a few, that map nicely with cryptographic requirements such as confusion, diffusion, deterministic pseudorandomness, algorithm complexity. Furthermore, the possibility of chaotic synchronization, where the master system (transmitter) is driving the slave system (receiver) by its output signal, made it probable for the possible utilization of chaotic systems to implement security in the communication systems. Many methods like chaotic masking, chaotic modulation, inclusion, chaotic shift keying (CSK) had been proposed however, many attack methods later showed them to be insecure. Different modifications of these methods also exist in the literature to improve the security, but almost all suffer from the same drawback. Therefore, the implementation of chaotic systems in security still remains a challenge. In this work, different possibilities on how it might be possible to improve the security of the existing methods are explored. The main problem with the existing methods is that the message imprint could be found in the dynamics of the transmitted signal, therefore by some signal processing or pattern classification techniques, etc, allow the exposition of the hidden message. Therefore, the challenge is to remove any pattern or change in dynamics that the message might bring in the transmitted signal

Design and implementation of secure chaotic communication systems

Chaotic systems have properties such as ergodicity, sensitivity to initial conditions/parameter mismatches, mixing property, deterministic dynamics, structure complexity, to mention a few, that map nicely with cryptographic requirements such as confusion, diffusion, deterministic pseudorandomness, algorithm complexity. Furthermore, the possibility of chaotic synchronization, where the master system (transmitter) is driving the slave system (receiver) by its output signal, made it probable for the possible utilization of chaotic systems to implement security in the communication systems. Many methods like chaotic masking, chaotic modulation, inclusion, chaotic shift keying (CSK) had been proposed however, many attack methods later showed them to be insecure. Different modifications of these methods also exist in the literature to improve the security, but almost all suffer from the same drawback. Therefore, the implementation of chaotic systems in security still remains a challenge. In this work, different possibilities on how it might be possible to improve the security of the existing methods are explored. The main problem with the existing methods is that the message imprint could be found in the dynamics of the transmitted signal, therefore by some signal processing or pattern classification techniques, etc, allow the exposition of the hidden message. Therefore, the challenge is to remove any pattern or change in dynamics that the message might bring in the transmitted signal.EThOS - Electronic Theses Online ServiceGBUnited Kingdo

Kernel - based continous - time systems identification: methods and tools

2012/2013Questa tesi ha lo scopo di formalizzare un nuovo filone teorico, che deriva dall’algebra degli operatori lineari integrali di Fredholm-Volterra agenti su spazi di Hilbert, per la sintesi di stimatori dello stato e parametrici per sistemi dinamici a tempo continuo sfruttando le misure ingressi/uscite, soggetti a perturbazione tempo-varianti. In maniera da ottenere stime non-asintotiche di sistemi dinamici a tempo continuo, i metodi classici tipicamente aumentano la dimensione del vettore delle variabili di decisione con le condizioni iniziali incognite di stati non misurati. Tuttavia, questo porta ad un accrescimento della complessitá dell’algoritmo. Recentemente, diversi metodi di stima algebrici sono stati sviluppati, sfruttando un approccio algebrico piuttosto che da una prospettiva statistica o teorica. Mentre le forti fondamenta teoriche e le proprietá di convergenza non asintotiche rappresentano caratteristiche notevoli per questi metodi, il principale inconveniente é che l’implementazione pratica produce una dinamica internamente instabile. Quindi, la progettazione di metodi di stima per questi tipi di sistemi é un argomento importante ed emergente. L’obiettivo di questo lavoro é quello di presentare alcuni risultati recenti, considerando diversi aspetti e affrontando alcuni dei problemi che emergono quando si progettano algoritmi di identificazione. Lo scopo é sviluppare un’architettura di stima con proprietá di convergenza molto veloci e internamente stabile. Seguendo un ordine logico, prima di tutto verrá progettato l’algoritmo di identificazione proponendo una nuova architettura basata sui kernel, utilizzando l’algebra degli operatori lineari integrali di Fredholm-Volterra. Inoltre, la metodologia proposta sará affrontata in maniera da progettare stimatori per sistemi dinamici a tempo continuo con proprietá di convergenza molto veloci, caratterizzati da gradi relativi limitati e possibilmente affetti da perturbazioni strutturate. Piú nello specifico, il progetto di adeguati kernel di operatori lineari integrali non-anticipativi dará origine a stimatori caratterizzati da proprietá di convergenza idealmente "non- asintotiche".Le analisi delle proprietá dei kernel verrá affrontata e due classi di funzioni kernel ammissibili saranno introdotte: una per il problema di stima parametrica e uno per il problema di stima dello stato. Gli operatori che verranno indotti da tali funzioni kernel proposte, ammettono realizzazione spazio-stato implementabile (cioé a dimensione finita e internamente stabile). Allo scopo di dare maggior completezza, l’analisi del bias dello stimatore proposto verrá esaminata, derivando le proprietá asintotiche dell’algoritmo di identificazione e dimostrando che le funzioni kernel possono essere pro- gettate tenendo in debito conto i risultati ottenuti in questa analisi.This thesis is aimed at the formalization of a new theoretical framework, arising from the algebra of Fredholm-Volterra linear integral operators acting on Hilbert spaces, for the synthesis of non-asymptotic state and parameter estimators for continuous-time dynamical systems from input-output measurements subject to time-varying perturbations. In order to achieve non-asymptotic estimates of continuous-time dynamical systems, classical methods usually augment the vector of decision variables with the unknown initial conditions of the non measured states. However, this comes at the price of an increase of complexity for the algorithm. Recently, several algebraic estimation methods have been developed, arising from an algebraic setting rather than from a statistical or a systems-theoretic perspective. While the strong theoretical foundations and the non-asymptotic convergence property represent oustanding features of these methods, the major drawback is that the practical implementation ends up with an internally unstable dynamic. Therefore, the design of estimation methods for these kind of systems is an important and emergent topic. The goal of this work is to present some recent results, considering different frameworks and facing some of the issues emerging when dealing with the design of identification algorithms. The target is to develop a comprehensive estimation architecture with fast convergence properties and internally stable. Following a logical order, first of all we design the identification algorithm by proposing a novel kernel-based architecture, by means of the algebra of Fredholm-Volterra linear integral operators. Besides, the proposed methodology is addressed in order to design estimators with very fast convergence properties for continuous-time dynamic systems characterized by bounded relative degree and possibly affected by structured perturbations. More specifically, the design of suitable kernels of non-anticipative linear integral operators gives rise to estimators characterized by convergence properties ideally “non-asymptotic". The analysis of the properties of the kernels guaranteeing such a fast convergence is addressed and two classes of admissible kernel functions are introduced: one for the parameter estimation problem and one for the state estimation problem. The operators induced by the proposed kernels admit implementable (i.e., finite-dimensional and internally stable) state- space realizations. For the sake of completeness, the bias analysis of the proposed estimator is addressed, deriving the asymptotic properties of the identification algorithm and demonstrating that the kernel functions can be designed taking in account the results obtained with this analysis.XXVI Ciclo198