Mehdi Roopaei

Synchronization of two different chaotic systems using novel adaptive fuzzy sliding mode control

In this paper, an adaptive fuzzy sliding mode control (AFSMC) scheme is proposed for the synchronization of two chaotic nonlinear systems in the presence of uncertainties and external disturbance. To design the reaching phase of the sliding mode control (SMC), a fuzzy controller is used. This will reduce the chattering and improve the robustness. An AFSMC is used (as an equivalent control part of the SMC) to approximate the unknown parts of the uncertain chaotic systems. Although the above schemes have been proposed in the past as separate stand-alone control schemes, in this paper, we integrate these methods to propose an effective control scheme having the benefits of each. The stability analysis for the proposed control scheme is provided and simulation examples are presented to verify the effectiveness of the method.

Adaptive gain fuzzy sliding mode control for the synchronization of nonlinear chaotic gyros

This paper proposes an adaptive gain fuzzy sliding mode control (AGFSMC) scheme for the synchronization of two nonlinear chaotic gyros in the presence of model uncertainties and external disturbances. In the AGFSMC scheme, the hitting controller that drives the system to the sliding surface is constructed by a set of fuzzy rules. In the proposed method, the gain of the reaching controller is adaptively adjusted to provide robustness against bounded uncertainties and external disturbances. The AGFSMC scheme can provide robustness in the absence of any knowledge about the bounds of uncertainties and external disturbances. We show that the adaptive gain scheme used in AGFSMC, improves the performance in comparison with the same control methodology that uses a fixed gain. Theoretical analysis of the AGFSMC scheme based on Lyapunov stability theory is provided. Numerical simulation on the application of the proposed method for the synchronization of two chaotic gyros is provided to demonstrate the feasibility of the method.

Synchronization of uncertain chaotic systems based on adaptive type-2 fuzzy sliding mode control

A novel direct adaptive interval type-2 fuzzy neural network (FNN) controller in which linguistic fuzzy control rules can be directly incorporated into the controller is developed to synchronize chaotic systems with training data corrupted by noise or rule uncertainties involving external disturbances, in this paper. By incorporating direct adaptive interval type-2 FNN control scheme and sliding mode approach, two non-identical chaotic systems can be synchronized based on Lyapunov stability criterion. Moreover, the chattering phenomena of the control efforts can be reduced and the external disturbance on the synchronization error can be attenuated. The stability of the proposed overall adaptive control scheme will be guaranteed in the sense that all the states and signals are uniformly bounded. From the simulation example, to synchronize two non-identical Chuas chaotic circuits, it has been shown that type-2 FNN controllers have the potential to overcome the limitations of tpe-1 FNN controllers when training data is corrupted by high levels of uncertainty.

Chaotic based reconstructed phase space features for detecting ventricular fibrillation

Abstract Among the variety of cardiac arrhythmias, ventricular fibrillation (VF) and ventricular tachycardia (VT) are life-threatening; thus, accurate classification of these arrhythmias is a crucial task for cardiologists. Nevertheless, VT and VF signals are very similar in the time domain and accurate distinguishing these signals with naked eyes in some cases is impossible. In this paper, a novel self-similarity image-based scheme is introduced to classify the underlying information of VT, VF and normal electrocardiogram (ECG) signals. In this study, VT, VF and normal ECG signals are selected from CCU of the Royal Infirmary of Edinburgh and MIT-BIH datasets. According to the time delay method, signal samples can be assigned to state variables and a trajectory can be achieved. To extract the proposed self-similarity feature, first, two different trajectories from each signal trial are drawn according to two different delay time values. The two-dimensional state space of each trial trajectory is considered as an image. Therefore, two trajectory images are produced for each signal. Number of visited pixels in the first image is determined and is subtracted from that of the second image as the self-similarity feature of that signal. Moreover, another scheme is proposed to have a better estimation of self-similarity in which the logical AND operator is applied to both images (matrices) of each ECG trial. The third proposed criterion is similar to box counting method by this difference that each pixel is assigned a weight according to the trajectory density at that point and finally visited weighted pixels are counted. To classify VF from VT and normal ECG, a threshold is determined through the cross validation phase under the Receiver Operating Characteristic (ROC) criterion. To assess the proposed methods, the mentioned signals are classified using the-state-of-art chaotic features such as correlation dimension, the largest Lyapunov exponent and Approximate Entropy (ApEn). Experimental results indicate superiority of the proposed method in classifying the VT, VF and normal ECG signals compared to present traditional schemes. In addition, computational complexity of the introduced methods is very low and can be implemented in real-time applications.

Synchronization of a class of chaotic systems with fully unknown parameters using adaptive sliding mode approach

In this paper, an adaptive sliding mode control method for synchronization of a class of chaotic systems with fully unknown parameters is introduced. In this method, no knowledge of the bounds of parameters is required in advance and the parameters are updated through an adaptive control process. We use our proposed method to synchronize two chaotic gyros, which has been the subject of intense study during the recent years for its application in the navigational, aeronautical, and space engineering domains. The effectiveness of our method is demonstrated in simulation environment and the results are compared with some recent schemes proposed in the literature for the same task.

Observer-based adaptive variable structure control and synchronization of unknown chaotic systems

Most physical chaotic systems inherently contain nonlinearities which are commonly unknown to the system designer. Therefore, in modeling and analysis of such chaotic systems, one needs to handle unknown nonlinearities and/or uncertain parameters. This paper addresses two new adaptive output feedback controllers for a large class of chaotic systems with unknown dynamics in presence of external disturbances. As a generalization of the control problem, synchronization of two uncertain chaotic systems is also investigated. In order to verify the effectiveness of the proposed methods, the methods are applied to Liu chaotic system.

Adaptive gain sliding mode control in uncertain MIMO systems

This paper addresses robust adaptive sliding mode control for MIMO nonlinear systems in the presence of uncertainties and external disturbances. To achieve stability and performance, we propose a sliding mode control scheme with the design of a gain, whose gain is not constant and need to be adaptively updated. Unlike some existing methods for sliding mode control, no knowledge on the bound of uncertainty and disturbance is required to be known and only the fixed points and the dimensions of uncertain nonlinear systems are required to be known for control purpose. The effectiveness of the proposed controller design methodology is demonstrated by simulations.

Adaptive control and synchronization in a class of partially unknown chaotic systems

This paper first addresses a novel control scheme to control a class of chaotic systems. In this method, no knowledge on the bounds of perturbations and disturbances is required in advance and parameters of the proposed controller are updated through an adaptive algorithm. Using the Lyapunov theory is employed to guarantee the stability of the closed loop system. Then synchronization of two nonidentical uncertain chaotic systems is investigated. To demonstrate the feasibility of the proposed scheme, numerical simulations on the application of control/synchronization of some famous chaotic systems are provided.

Adaptive type-2 fuzzy sliding mode control for chaos synchronization of uncertain chaotic systems

This paper a novel adaptive interval type-2 fuzzy neural network (FNN) controller is proposed to synchronize chaotic systems with training data corrupted by noise or rule uncertainties involving external disturbances. Adaptive interval type-2 FNN control scheme and sliding mode approach are incorporated to deal with the synchronization of non-identical chaotic systems. In the meantime, the Lyapunov stability theorem has been used to testify the asymptotic stability of the chaotic systems, based on the adaptive fuzzy sliding mode control. The chattering phenomena in the control efforts can be reduced and the stability analysis of the proposed control scheme will be guaranteed in the sense that all the states and signals are uniformly bounded and the external disturbance on the synchronization error can be attenuated. The simulation example is included to confirm validity and performance of the advocated design methodology.

Stable adaptive synchronization of a class of uncertain time-delay chaotic systems via H ∞ type-2 FNN control

In this paper, a new direct adaptive interval type-2 fuzzy controller is proposed to synchronize between two different chaotic time-delay systems with noisy training data or rule uncertainties. Based on the adaptive time-delay interval type-2 fuzzy logic systems in which linguistic fuzzy control rules can be directly incorporated into the controller and by adjusting weights, centers and widths, the modeling and synchronization errors can be eliminated by using H∞ tracking approach. It is shown that a master time-delay chaotic system with the desired system dynamics is used as a reference model for the output of slave time-delay chaotic system to track. The simulation example is included to confirm validity and performance of the advocated design methodology.