Adaptive unknonwn-input observers-based synchronization of chaotic circuits for secure telecommunication

International audienceWe propose a robust adaptive chaotic synchronization method based on unknown-input observers for master-slave syn- chronization of chaotic systems, with application to secured com- munication. The slave system is modelled by an unknown input observer in which, the unknown input is the transmitted informa- tion. As in the general observer-based synchronization paradigm, the information is recovered if the master and slave systems ro- bustly synchronize. In the context of unknown-input observers, this is tantamount to estimating the master's states and the unknown inputs. The set-up also considers the presence of perturbations in the chaotic transmitter dynamics and in the output equations (the transmitted signal). That is, the estimator (slave system) must syn- chronize albeit noisy measurements and reject the effect of pertur- bations on the transmitter dynamics. We provide necessary and sufficient conditions for synchronization to take place. To highlight our contribution, we also present some simulation results with the purpose of comparing the proposed method to classical adaptive observer-based synchronization (without disturbance rejection). It is shown that additive noise is perfectly canceled and the encoded message is well recovered despite the perturbations

Dynamic system with no equilibrium and its chaos anti-synchronization

Recently, systems with chaos and the absence of equilibria have received a great deal of attention. In our work, a simple five-term system and its anti-synchronization are presented. It is special that the system has a hyperbolic sine nonlinearity and no equilibrium. Such a system generates chaotic behaviours, which are verified by phase portraits, positive Lyapunov exponent as well as an electronic circuit. Moreover, the system displays multistable characteristic when changing its initial conditions. By constructing an adaptive control, chaos anti-synchronization of the system with no equilibrium is obtained and illustrated via a numerical example

A Chaotic System with an Infinite Number of Equilibrium Points: Dynamics, Horseshoe, and Synchronization

Discovering systems with hidden attractors is a challenging topic which has received considerable interest of the scientific community recently. This work introduces a new chaotic system having hidden chaotic attractors with an infinite number of equilibrium points. We have studied dynamical properties of such special system via equilibrium analysis, bifurcation diagram, and maximal Lyapunov exponents. In order to confirm the system’s chaotic behavior, the findings of topological horseshoes for the system are presented. In addition, the possibility of synchronization of two new chaotic systems with infinite equilibria is investigated by using adaptive control

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

A stability-theory perspective to synchronisation of heterogeneous networks

Dans ce mémoire, nous faisons une présentation de nos recherches dans le domaine de la synchronisation des systèmes dynamiques interconnectés en réseau. Une des originalités de nos travaux est qu'ils portent sur les réseaux hétérogènes, c'est à dire, des systèmes à dynamiques diverses. Au centre du cadre d'analyse que nous proposons, nous introduisons le concept de dynamique émergente. Il s'agit d'une dynamique "moyennée'' propre au réseau lui-même. Sous l'hypothèse qu'il existe un attracteur pour cette dynamique, nous montrons que le problème de synchronisation se divise en deux problèmes duaux : la stabilité de l'attracteur et la convergence des trajectoires de chaque système vers celles générées par la dynamique émergente. Nous étudions aussi le cas particulier des oscillateurs de Stuart-Landau

Discrete Time Systems

Discrete-Time Systems comprehend an important and broad research field. The consolidation of digital-based computational means in the present, pushes a technological tool into the field with a tremendous impact in areas like Control, Signal Processing, Communications, System Modelling and related Applications. This book attempts to give a scope in the wide area of Discrete-Time Systems. Their contents are grouped conveniently in sections according to significant areas, namely Filtering, Fixed and Adaptive Control Systems, Stability Problems and Miscellaneous Applications. We think that the contribution of the book enlarges the field of the Discrete-Time Systems with signification in the present state-of-the-art. Despite the vertiginous advance in the field, we also believe that the topics described here allow us also to look through some main tendencies in the next years in the research area

Third-order robust fuzzy sliding mode tracking control of a double-acting electrohydraulic actuator

In the industrial sector, an electrohydraulic actuator (EHA) system is a common technology. This system is often used in applications that demand high force, such as the steel, automotive, and aerospace industries. Furthermore, since most mechanical actuators' performance changes with time, it is considerably more difficult to assure its robustness over time. Therefore, this paper proposed a robust fuzzy sliding mode proportional derivative (FSMCPD) controller. The sliding mode controller (SMC) is accomplished by utilizing the exponential law and the Lyapunov theorem to ensure closed loop stability. By replacing the fuzzy logic control (FLC) function over the signum function, the chattering in the SMC controller has been considerably reduced. By using the sum of absolute errors as the objective function, particle swarm optimization (PSO) was used to optimize the controller parameter gain. The experiment results for trajectory tracking and the robustness test were compared with the sliding mode proportional derivative (SMCPD) controller to demonstrate the performance of the FSMCPD controller. According to the findings of the thorough study, the FSMCPD controller outperforms the SMCPD controller in terms of mean square error (MSE) and robustness index (RI)

Criptografia baseada em caos : aplicação usando um sistema hipercaótico

Trabalho de conclusão de curso (graduação)—Universidade de Brasília, Faculdade de Tecnologia, Departamento de Engenharia Elétrica, 2019.Neste trabalho se propõe um esquema para telecomunicação segura baseado na sincroni zação de um sistema nonodimensional hipercaotico e analise de Lyapunov. Ao contrário da maioria dos esquemas usualmente encontrados na literatura, o esquema proposto requer apenas que o controle atue em uma das equações de estado do sistema escravo. Foi verificada mate maticamente a convergência do erro de sincronização para um conjunto compacto arbitrário, permitindo-se obter um erro convergente a uma vizinhança da origem. Com um circuito caótico transmissor (ou mestre) codifica-se o sinal (ou mensagem) e com outro circuito caótico receptor (ou escravo) recupera-se a mensagem. O esquema proposto tem como vantagens ser robusto contra perturbações (internas e externas) e ser estruturalmente simples, quando comparado com as propostas existentes na literatura, o que é importante, uma vez que leva a redução de custos quando implementado utilizando eletrônica analógica. Para validar a robustez e simplicidade do esquema proposto, simulações computacionais utilizando software MATLAB/Simulink foram realizadas.This work proposes a scheme for secure telecommunication based on the synchronization of a hyperchaotic system and Lyapunov analysis. Unlike most schemes usually found in the literature, the proposed scheme only requires that the control act on one of the slave state equa tions. The convergence of the synchronization error to an arbitrary compact set was verified mathematically, allowing a convergent error to be arbitrarily small neighborhood of the origin. With a transmitting (or master) chaotic circuit the signal (or message) is encoded and with another receiving (or slave) chaotic circuit the message is retrieved. The proposed scheme has the advantages of being robust against disturbances (internal and external) and being structu rally simple when compared to the existing proposals in the literature, which is important as it leads to cost savings when implemented using analog electronics. To validate the robust ness and simplicity of the proposed scheme, computer simulations using MATLAB/Simulink software were performed

Synchronization of complex dynamical networks with fractional order

Complex dynamical networks (CDN) can be applied to many areas in real world, from medicine, biology, Internet to sociology. Study on CDNs has drawn great attention in recent years. Nodes in a CDN can be modelled as systems represented by differential equations. Study has shown that fractional order differential equations (DF) can better represent some real world systems than integer-order DFs. This research work focuses on synchronization in fractional CDNs.  A literature review on CDNs with fractional order has summarized the latest works in this area.  Fractional chaotic systems are studied in our initial investigation.  Fractional calculus is introduced and the relevant fundamentals to model, describe and analyse dynamical networks are presented. It is shown that the structure and topological characteristics of a network can have a big impact on its synchronizability. Synchronizability and its various interpretations in dynamical networks are studied. To synchronize a CDN efficiently, controllers are generally needed. Controller design is one of the main tasks in this research. Our first design is a new sliding mode control to synchronize a dynamical network with two nodes. Its stability has been proven and verified by simulations.  Its convergence speed outperforms Vaidyanathan's scheme, a well-recognized scheme in this area. The design can be generalized to CDNs with more nodes.  As many applications can be modelled as CDNs with node clustering, a different sliding mode control is designed for cluster synchronization of a CDN with fractional order. Its stability is proven by using Lyapunov method. Its convergence and efficiency is shown in a simulation. Besides these nonlinear methods mentioned, linear control is also studied intensively for the synchronization.  A novel linear method for synchronization of fractional CDNs using a new fractional Proportional-Integral (PI) pinning control is proposed.  Its stability is proven and the synchronization criteria are obtained. The criteria have been simplified using two corollaries so the right value for the variables can be easily assigned. The proposed method is compared with the conventional linear method which uses Proportional (P) controller. In the comparison, the mean squared error function is used. The function measures the average of the squared errors and it is an instant indicator of the synchronization efficiency. A numerical simulation is repeated 100 times to obtain the averages over these runs. Each simulation has different random initial values for both controllers. The average of the errors in all the 100 simulations is obtained and the area under the function curve is defined as an overall performance index (OPI), which indicates the controller's overall performance. In control, small overshoot is always desired. In our work, the error variation is also used as a measure.  The maximum variation from the average of 100 simulations is calculated and compared for both methods. With all the statistical comparisons, it is clear that with the same power consumption, the proposed method outperforms the conventional one and achieves faster and smoother synchronization. Communication constraints exist in most real world CDNs. Communication constraints and their impact on control and synchronization of CDNs with fractional order are investigated in our study. A new adaptive method for synchronizing fractional CDN with disturbance and uncertainty is designed. Its stability is proven and its synchronization criteria are obtained for both fractional CDN with known and unknown parameters. Random disturbance is also included in both cases. Our results show that the new method is efficient in synchronizing CDNs with presence of both disturbance and uncertainty