Abstract: This work addresses the problem of designing an
algorithm capable of generating chaotic trajectories for mobile robots.
Particularly, the chaotic behavior is induced in the linear and angular
velocities of a Khepera III differential mobile robot by infusing them
with the states of the H´enon chaotic map. A possible application,
using the properties of chaotic systems, is patrolling a work area.
In this work, numerical and experimental results are reported and
analyzed. In addition, two quantitative numerical tests are applied in
order to measure how chaotic the generated trajectories really are.
Abstract: In this paper, the finite-time symplectic synchronization
between two different chaotic systems is investigated. Based on the
finite-time stability theory, a simple adaptive feedback scheme is
proposed to realize finite-time symplectic synchronization for the
Lorenz and L¨u systems. Numerical examples are provided to show
the effectiveness of the proposed method.
Abstract: In this paper, an encryption algorithm is proposed for real-time image encryption. The scheme employs a dual chaotic generator based on a three dimensional (3D) discrete Lorenz attractor. Encryption is achieved using non-autonomous modulation where the data is injected into the dynamics of the master chaotic generator. The second generator is used to permute the dynamics of the master generator using the same approach. Since the data stream can be regarded as a random source, the resulting permutations of the generator dynamics greatly increase the security of the transmitted signal. In addition, a technique is proposed to mitigate the error propagation due to the finite precision arithmetic of digital hardware. In particular, truncation and rounding errors are eliminated by employing an integer representation of the data which can easily be implemented. The simple hardware architecture of the algorithm makes it suitable for secure real-time applications.
Abstract: In this paper, Backstepping method is proposed to synchronize two fractional-order systems. The simulation results show that this method can effectively synchronize two chaotic systems.
Abstract: This paper presents a new nonlinear integral-type sliding surface for synchronizing two different chaotic systems with parametric uncertainty. On the basis of Lyapunov theorem and average dwelling time method, we obtain the control gains of controllers which are derived to achieve chaos synchronization. In order to reduce the gains, the error system is modeled as a switching system. We obtain the sufficient condition drawn for the robust stability of the error dynamics by stability analysis. Then we apply it to guide the design of the controllers. Finally, numerical examples are used to show the robustness and effectiveness of the proposed control strategy.
Abstract: In chaos synchronization, the main goal is to design such controller(s) that synchronizes the states of master and slave system asymptotically globally. This paper studied and investigated the synchronization problem of two identical Chen, and identical Tigan chaotic systems and two non-identical Chen and Tigan chaotic systems using Non-linear active control algorithm. In this study, based on Lyapunov stability theory and using non-linear active control algorithm, it has been shown that the proposed schemes have excellent transient performance using only two nonlinear controllers and have shown analytically as well as graphically that synchronization is asymptotically globally stable.
Abstract: A gradient learning method to regulate the trajectories
of some nonlinear chaotic systems is proposed. The method is
motivated by the gradient descent learning algorithms for neural
networks. It is based on two systems: dynamic optimization system
and system for finding sensitivities. Numerical results of several
examples are presented, which convincingly illustrate the efficiency
of the method.
Abstract: Based on general proportional integral (GPI) observers and sliding mode control technique, a robust control method is proposed for the master-slave synchronization of chaotic systems in the presence of parameter uncertainty and with partially measurable output signal. By using GPI observer, the master dynamics are reconstructed by the observations from a measurable output under the differential algebraic framework. Driven by the signals provided by GPI observer, a sliding mode control technique is used for the tracking control and synchronization of the master-slave dynamics. The convincing numerical results reveal the proposed method is effective, and successfully accommodate the system uncertainties, disturbances, and noisy corruptions.
Abstract: In this paper, encrypted audio communications based on synchronization of coupled unified chaotic systems in master-slave configuration is numerically studied. We transmit the encrypted audio messages by using two unsecure channels. Encoding, transmission, and decoding audio messages in chaotic communication is presented.
Abstract: In this paper, a two-channel secure communication
using fractional chaotic systems is presented. Conditions for chaos
synchronization have been investigated theoretically by using Laplace
transform. To illustrate the effectiveness of the proposed scheme, a
numerical example is presented. The keys, key space, key selection
rules and sensitivity to keys are discussed in detail. Results show that
the original plaintexts have been well masked in the ciphertexts yet
recovered faithfully and efficiently by the present schemes.
Abstract: One of the most attractive and important field of chaos theory is control of chaos. In this paper, we try to present a simple framework for chaotic motion control using the feedback linearization method. Using this approach, we derive a strategy, which can be easily applied to the other chaotic systems. This task presents two novel results: the desired periodic orbit need not be a solution of the original dynamics and the other is the robustness of response against parameter variations. The illustrated simulations show the ability of these. In addition, by a comparison between a conventional state feedback and our proposed method it is demonstrated that the introduced technique is more efficient.
Abstract: A new strategy of control is formulated for chaos synchronization of non-identical chaotic systems with different orders using the Borne and Gentina practical criterion associated with the Benrejeb canonical arrow form matrix, to drift the stability property of dynamic complex systems. The designed controller ensures that the state variables of controlled chaotic slave systems globally synchronize with the state variables of the master systems, respectively. Numerical simulations are performed to illustrate the efficiency of the proposed method.
Abstract: This paper presents anti-synchronization of chaos
between two different chaotic systems using active control method.
The proposed technique is applied to achieve chaos antisynchronization
for the Lü and Rössler dynamical systems.
Numerical simulations are implemented to verify the results.
Abstract: Many systems in the natural world exhibit chaos or non-linear behavior, the complexity of which is so great that they appear to be random. Identification of chaos in experimental data is essential for characterizing the system and for analyzing the predictability of the data under analysis. The Lyapunov exponents provide a quantitative measure of the sensitivity to initial conditions and are the most useful dynamical diagnostic for chaotic systems. However, it is difficult to accurately estimate the Lyapunov exponents of chaotic signals which are corrupted by a random noise. In this work, a method for estimation of Lyapunov exponents from noisy time series using unscented transformation is proposed. The proposed methodology was validated using time series obtained from known chaotic maps. In this paper, the objective of the work, the proposed methodology and validation results are discussed in detail.
Abstract: This paper presents a method for functional projective H∞ synchronization problem of chaotic systems with external disturbance. Based on Lyapunov theory and linear matrix inequality (LMI) formulation, the novel feedback controller is established to not only guarantee stable synchronization of both drive and response systems but also reduce the effect of external disturbance to an H∞ norm constraint.
Abstract: In this paper, a new dependable algorithm based on an adaptation of the standard variational iteration method (VIM) is used for analyzing the transition from steady convection to chaos for lowto-intermediate Rayleigh numbers convection in porous media. The solution trajectories show the transition from steady convection to chaos that occurs at a slightly subcritical value of Rayleigh number, the critical value being associated with the loss of linear stability of the steady convection solution. The VIM is treated as an algorithm in a sequence of intervals for finding accurate approximate solutions to the considered model and other dynamical systems. We shall call this technique as the piecewise VIM. Numerical comparisons between the piecewise VIM and the classical fourth-order Runge–Kutta (RK4) numerical solutions reveal that the proposed technique is a promising tool for the nonlinear chaotic and nonchaotic systems.
Abstract: In this paper, a generalized synchronization scheme, which is called function synchronization, for chaotic systems is studied. Based on Lyapunov method and active control method, we design the synchronization controller for the system such that the error dynamics between master and slave chaotic systems is asymptotically stable. For verification of our theory, computer and circuit simulations for a specific chaotic system is conducted.
Abstract: Chua’s circuit is one of the most important electronic devices that are used for Chaos and Bifurcation studies. A central role of secure communication is devoted to it. Since the adaptive control is used vastly in the linear systems control, here we introduce a new trend of application of adaptive method in the chaos controlling field. In this paper, we try to derive a new adaptive control scheme for Chua’s circuit controlling because control of chaos is often very important in practical operations. The novelty of this approach is for sake of its robustness against the external perturbations which is simulated as an additive noise in all measured states and can be generalized to other chaotic systems. Our approach is based on Lyapunov analysis and the adaptation law is considered for the feedback gain. Because of this, we have named it NAFT (Nonlinear Adaptive Feedback Technique). At last, simulations show the capability of the presented technique for Chua’s circuit.
Abstract: This paper at first presents approximate analytical
solutions for systems of fractional differential equations using the
differential transform method. The application of differential
transform method, developed for differential equations of integer
order, is extended to derive approximate analytical solutions of
systems of fractional differential equations. The solutions of our
model equations are calculated in the form of convergent series with
easily computable components. After that a drive-response
synchronization method with linear output error feedback is
presented for “generalized projective synchronization" for a class of
fractional-order chaotic systems via a scalar transmitted signal.
Genesio_Tesi and Duffing systems are used to illustrate the
effectiveness of the proposed synchronization method.
Abstract: In this paper, a fuzzy controller is designed for
stabilization of the Lorenz chaotic equations. A simple Mamdani
inference method is used for this purpose. This method is very simple
and applicable for complex chaotic systems and it can be
implemented easily. The stability of close loop system is investigated
by the Lyapunov stabilization criterion. A Lyapunov function is
introduced and the global stability is proven. Finally, the
effectiveness of this method is illustrated by simulation results and it
is shown that the performance of the system is improved.