Chaotic Systems In Presence Research Articles

Novel Single Bounded Input Control Synchronization Criterion for a Category of Hyperchaotic and Chaotic Systems in Presence of Uncertainties

Abstract Dynamical systems that have a chaotic underlying structure have a sensitive dependency on the initial conditions and the values of their parameters. In this piece of work, a straightforward method for solving the synchronization issue in master–slave arrangement for a category of chaotic or hyperchaotic systems, in which perturbations are present in the parameters of the response system, is discussed. The desired control signal is bounded by the initial state when the controller is activated. There is just one control input that is used, and it is derived from Lyapunov's concept of stability. In general, it is tricky to synchronize hyperchaotic or chaotic systems with single controller, and the work turns out to be significantly more complex when the parameters of the slave system are perturbed. The feedback controller using single input that has been constructed makes certain that the state variables of the response system are in synchronization with the state variables that correspond to them in the drive system. In order to attain the desired level of synchronization, the required conditions that must be satisfied to do so have been identified utilizing Lyapunov's stability analysis in a simple manner. In addition, numerical illustrations have been provided in order to support and confirm the theoretical findings of the paper.

A Novel Approach for Synchronizing of Fractional Order Uncertain Chaotic Systems in the Presence of Unknown Time-Variant Delay and Disturbance

This paper presents a new method for synchronizing between two fractional order chaotic systems in the simultaneous presence of three categories including uncertainty, external disturbance and time-varying delay. The uncertainties considered in chaotic drive and response systems are on the nonlinear functions, the external disturbances are finite with unknown upper bound, and the delays in the nonlinear functions are 1- variable with time 2- unknown and 3- different from each other in two drive and response systems. A new hybrid method based on fuzzy, adaptive and robust techniques is proposed to achieve synchronization for a specific class of fractional order chaotic systems. The fuzzy method is used to estimate the effects of uncertainties and delayed functions, the adaptive method is employed to obtain the optimal weights of the fuzzy approximator as well as the estimation for upper bound of disturbances, and the robust method is performed to ensure the stability of synchronization and also to cover the errors of both fuzzy and adaptive methods. Simulation in MATLAB environment shows the efficiency of the proposed method in achieving the synchronization goal despite the problems of delay, disturbance and uncertainty.

Finite-time fractional-order adaptive intelligent backstepping sliding mode control of uncertain fractional-order chaotic systems

This paper precedes chaos control of fractional-order chaotic systems in presence of uncertainty and external disturbances. Based on some basic properties on fractional calculus and the stability theorems, we present a hybrid adaptive intelligent backstepping-sliding mode controller (FAIBSMC) for the finite-time control of such systems. The FAIBSMC is proposed based on the concept of active control technique. The asymptotic stability of the controller is shown based on Lyapunov theorem and the finite time reaching to the sliding surfaces is also proved. Illustrative and comparative examples and simulation results are given to confirm the effectiveness of the proposed procedure, which consent well with the analytical results.

Synchronization of Time-Delay Chaotic System in Presence of Noise

Abstract Chaotic synchronization, as a key technique of chaotic secure communication, has received much attention in recent years. This paper proposes a nonlinear synchronization scheme for the time-delay chaotic system in the presence of noise. In this scheme, an integrator is introduced to suppress the influence of channel noise in the synchronization process. The experimental results demonstrate the effectiveness and feasibility of the proposed scheme which is strongly robust against noises, especially the high-frequency noises.

Application of particle swarm optimization in chaos synchronization in noisy environment in presence of unknown parameter uncertainty

In this paper, particle swarm optimization (PSO) is applied to synchronize chaotic systems in presence of parameter uncertainties and measurement noise. Particle swarm optimization is an evolutionary algorithm which is introduced by Kennedy and Eberhart. This algorithm is inspired by birds flocking. Optimization algorithms can be applied to control by defining an appropriate cost function that guarantees stability of system. In presence of environment noise and parameter uncertainty, robustness plays a crucial role in succeed of controller. Since PSO needs only rudimentary information about the system, it can be a suitable algorithm for this case. Simulation results confirm that the proposed controller can handle the uncertainty and environment noise without any extra information about them. A comparison with some earlier works is performed during simulations.

Stochastic chaos synchronization using Unscented Kalman–Bucy Filter and sliding mode control

This paper presents an algorithm for synchronizing two different chaotic systems by using a combination of Unscented Kalman–Bucy Filter (UKBF) and sliding mode controller. It is assumed that the drive chaotic system is perturbed by white noise and shows stochastic chaotic behavior. In addition the output of the system does not contain the whole state variables of the system, and it is also affected by some independent white noise. By combining the UKBF and the sliding mode control, a synchronizing control law is proposed. Simulation results show the ability of the proposed method in synchronizing chaotic systems in presence of noise.

Synchronization of two different chaotic systems using novel adaptive interval type-2 fuzzy sliding mode control

In this paper, we use sliding mode control integrated with an interval type-2 fuzzy system for synchronization of two different chaotic systems in presence of system unmodeling and external disturbances. To reduce the chattering and improve the robustness of reaching phase of the Sliding Mode Control (SMC), an interval fuzzy type-2 logic controller is used. In addition, an adaptive interval type-2 fuzzy inference approximator is proposed (as equivalent control part of SMC) to approximate the unknown parts of the uncertain chaotic system. Using type-2 fuzzy systems makes more effective synchronization results in presence of system uncertainty and disturbances in comparison with type-1 fuzzy approximators. The stability analysis for the proposed control scheme is provided, and simulation results compare the performance of interval type-2 fuzzy and type-1 fuzzy controllers to verify the effectiveness of the proposed method.

Chaos synchronization in noisy environment using nonlinear filtering and sliding mode control

This paper presents an algorithm for synchronizing two different chaotic systems, using a combination of the extended Kalman filter and the sliding mode controller. It is assumed that the drive chaotic system has a random excitation with a stochastically chaotic behavior. Two different cases are considered in this study. At first it is assumed that all state variables of the drive system are available, i.e. complete state measurement, and a sliding mode controller is designed for synchronization. For the second case, it is assumed that the output of the drive system does not contain the whole state variables of the drive system, and it is also affected by some random noise. By combination of extended Kalman filter and the sliding mode control, a synchronizing control law is proposed. As a case study, the presented algorithm is applied to the Lur’e-Genesio chaotic systems as the drive-response dynamic systems. Simulation results show the good performance of the algorithm in synchronizing the chaotic systems in presence of noisy environment.