Class Of Nonlinear Chaotic Systems Research Articles

Reduced Order Observer Based Synchronization and Secure Communication for a Class of Nonlinear Chaotic Systems

Reduced Order Observer Based Synchronization and Secure Communication for a Class of Nonlinear Chaotic Systems

Adaptive fuzzy finite-time PID backstepping control for chaotic systems with full states constraints and unmodeled dynamics

To solve the problem that the controlled object and system model cannot be fully mastered or the system parameters cannot be well obtained through conventional measurement methods, in this paper, a novel adaptive fuzzy finite-time PID backstepping control method is developed for a class of nonlinear chaotic systems with full state constraints and unmodeled dynamics. The unmodeled dynamics are handled by employing a dynamic signal. To avoid the violations of full state constraints (FSCs), a barrier Lyapunov function is used to implement a PID backstepping framework, whose merit consists in that three control gain constants KP, KI and KD with corresponding proportional relationships are designed to further improve control precision. Besides, the PID control method also embodies three dynamic gain components ΔKP, ΔKI and ΔKD, all of which are free functions that can be self-tuning online, and have a significant link with the adaptive law and modify accordingly. Finally, theoretical analysis confirms that all signals are ultimately uniformly bounded, the error signal converges to a nearby area near the origin in a finite-time, and the FSCs are not smashed. The practicality of the proposed method is confirmed by two simulation studies using the second-order Duffing chaotic system and third-order Chua's circuit.

Finite time super twisting controller based on adaptive dual-layer disturbance observer for synchronisation of nonlinear chaotic systems

The present article proposes a novel finite-time dual-layer disturbance observer-based controller with the aim of addressing the synchronisation problem for a class of nonlinear chaotic systems experiencing unmodelled dynamics and external disturbances. The adaptive finite-time synchronisation between perturbed drive and response systems is obtained by means of higher order super-twisting terminal sliding mode control (SMC) strategy. The main innovative part of this work is the proposition of a newly designed adaptive finite-time dual-layer estimator (DLE) with two-level observation to exactly estimate the imposed perturbations on the both drive and response systems considering unknown upper bounds. The estimated signals are utilised in the proposed continuous super-twisting sliding mode controller for the purpose of addressing robust finite-time synchronisation problem for a class of chaotic systems. Numerical simulations and achieved results are illustrated to present the efficiency of the investigated approaches.

Adaptive control for a class of nonlinear chaotic systems with quantized input delays

This paper proposes adaptive prediction-based control design for nonlinear chaotic systems in the presence of input quantization with actuator delay. A class of sector-bounded quantizer, namely the hysteresis quantizer, has been used to quantize the control signal. Adaptive scheme is utilized to estimate unknown parameters of the nonlinear chaotic system. A new prediction vector is introduced to compensate actuator delay for nonlinear systems with unknown parameters. The proposed controller does not require the restrictive conditions for quantized parameters in contrast to some existing control schemes for systems with input quantization. By error analysis, it is insured that the upper bound of the state vector norm is limited. Moreover, a maximum allowable upper bound for actuator time-delay is achieved and is guaranteed that for any input delay less than this value, the closed-loop system is stable. To show the efficiency of the proposed method, it is applied to brushless DC motor and Chua’s circuit with delayed hysteresis input and compared to the existing results in the literature. Simulation results show that the proposed method is able to compensate actuator time-delay with hysteresis quantized input for a class of nonlinear systems having unknown parameters. The robustness and efficiency of the suggested approach are illustrated by comparative simulation results.

Hybrid control strategy applied to chaos synchronization: new control design and stability analysis

This paper proposes a hybrid control strategy for synchronization of a class of nonlinear chaotic systems by incorporating sliding mode control (SMC) and state feedback control (SFC) techniques via fuzzy logic. This fuzzy system makes a decision when to utilize every one of the controllers or a combination of them. The main aspect of the controller proposed in this paper is twofold: (1) controller design and stability analysis provided by the Lyapunov theory are straightforward; (2) it attenuates significantly inherent chattering in the control effort. An illustrative example for the synchronization of chaotic gyro system is implemented to verify the efficiency of the proposed controller. Results demonstrate the preference of the proposed control method compared with SMC technique.

Adaptive Neural Gradient Descent Control for a Class of Nonlinear Dynamic Systems with Chaotic Phenomenon

A neural network controller design is studied for a class of nonlinear chaotic systems with uncertain parameters. Because the chaos phenomena are often in this class of systems, it is indispensable to control this class of systems. At the same time, due to the presence of uncertainties in the chaotic systems, it results in the difficulties of the controller design. The neural networks are employed to estimate the uncertainties of the systems and a controller is designed to overcome the chaos phenomena. The main contribution of this paper is that the adaptation law can be determined via the gradient descent algorithm to minimize a cost function of error. It can prove the stability of the closed-loop system. The numerical simulation is specified to pinpoint the validation of the approach.

A robust and simple optimal type II fuzzy sliding mode control strategy for a class of nonlinear chaotic systems

This paper suggests a new hybrid control strategy, called Optimal Type II Fuzzy Sliding Mode (OT2FSM) control scheme, to realize the control of general uncertain chaotic systems. The proposed controller not only guaranties the stability and robustness against the lumped uncertainties caused by unmodeled dynamics and external disturbances, but also can significantly reduce the control chattering inherent in conventional sliding mode control. In the proposed controller, a novel heuristic algorithm namely particle swarm optimization with random inertia weight (RNW–PSO) is employed. To achieve an optimal performance, the parameters of the proposed controller as well as the input and output membership functions are optimized simultaneously by RNW–PSO. The globally asymptotic stability of the closed-loop system is mathematically proved. To evaluate the performance of the proposed controller, the results are compared with those obtained by Optimal H-infinity Adaptive PID (OHAPID) controller and an optimal Type-2 fuzzy proportional integral derivative (OT2FPID), which are the latest researches in the problem in hand. Simulation results show the effectiveness of the OT2FSM controller.

Synchronization of Continuous Scalar Chaotic Signal from Uncertain Chaotic System

This paper presents the synchronizing problem of scalar chaotic signal. A class of nonlinear chaotic systems is discussed which has unknown part in model. The proposed approach is based on canonical form of the response system. Simulation result shows the effectiveness of our synchronization scheme.

Synchronization of nonlinear systems with delays via periodically nonlinear intermittent control

In this paper, the synchronization for a class of nonlinear chaotic systems with delays is proposed by using periodically intermittent nonlinear feedback control. Some synchronization criteria are derived based on Lyapunov functional theory and several differential inequalities such as Halanay inequality. As a special case, some sufficient conditions are obtained to ensure the synchronization of nonlinear systems without delays. Finally, some numerical simulations are presented to verify the theoretical results.

Reliable impulsive synchronization for a class of nonlinear chaotic systems

The problem of reliable impulsive synchronization for a class of nonlinear chaotic systems has been investigated in this paper. Firstly a reliable impulsive controller is designed by using the impulsive control theory. Then by the uniform asymptotic stability criteria of systems with impulsive effects, some sufficient conditions for reliable impulsive synchronization between the drive system and the response system are obtained. Numerical simulations are given to show the effectiveness of the proposed method.

Reduced-order adaptive control design for the stabilization and synchronization of a class of nonlinear chaotic systems

Strategies to design reduced-order adaptive controllers using only part of the system states for the stabilization of one chaotic system and the synchronization of two chaotic systems are proposed for a general class of chaotic systems. Compared with those existed results, the adaptive controllers presented in this paper can globally exponentially stabilize the chaotic systems and can globally exponentially synchronize the two chaotic systems under certain conditions, and therefore can improve the convergence rate of the control processes. Simulation results also verify the effectiveness of the proposed control schemes.

ROBUST LINEAR OUTPUT FEEDBACK CONTROL DESIGN FOR NONLINEAR CHAOTIC SYSTEMS VIA T–S FUZZY MODEL WITH H∞ SETTING

In this paper, the problem of H∞ control design is studied for a nonlinear chaotic system via its corresponding Takagi–Sugeno (T–S) fuzzy model. It is known that many nonlinear chaotic systems can be exactly represented by their corresponding T–S fuzzy models. First, in this study, the T–S fuzzy model is proposed to represent a class of nonlinear chaotic systems. Next, a linear output feedback control scheme, where only linear controller and linear observer are considered, with H∞ setting is proposed for the nonlinear chaotic system. Then, based on the T–S fuzzy model and the proposed linear control scheme, the H∞ controller design problem for nonlinear chaotic systems is characterized in terms of minimizing the attenuation level subject to some linear matrix inequalities (LMIs), which is also called eigenvalue problem (EVP), through the scanning of a positive parameter. Finally, the proposed control scheme is applied to a chaotic system, namely Chua's circuit, to illustrate the robust performance of the proposed linear controller and linear observer.

Chaotic synchronization and secure communication based on descriptor observer

This paper presents an effective technique for both synchronization and secure communication of chaotic systems. A class of nonlinear chaotic systems is discussed, whose transmitted signal can be of multiple dimensions. Based on the descriptor observer design, we can obtain the accurate estimations of both the system states and the transmitted signals. Because the descriptor observer approach avoids using the derivation of the transmitted signal, the approach proposed does not need the assumption that the information signal is slowly varying. Numerical examples are given to illustrate the effectiveness of the proposed scheme.

Design of model-based controllers for a class of nonlinear chaotic systems using a single output feedback and state observers

A model-based control methodology for suppressing chaos for nonlinear systems is introduced. The proposed methodology generates new periodic orbits or steady states, which are not the solutions of the free system, using output feedback and state observers. The design uses the certainty equivalence principle to construct a linear closed loop system that can follow desired outputs with zero steady state offsets via using a pole-placement-like approach. The combined dynamics of both the controller and the state observer are carefully studied using the well-known Rössler system. The similarities and differences between the proposed control technique and both the double-notch filter feedback and the time-delay autosynchronization are investigated. The effect of parameter uncertainties is studied and robustness of the proposed controller is analyzed.

Complete inverse chaos synchronization, parameter mismatches and generalized synchronization in the multi-feedback Ikeda model

We investigate complete inverse synchronization between two uni-directionally coupled chaotic multi-feedback Ikeda systems and find its existence and stability conditions. We also study generalized synchronization between two uni-directionally coupled chaotic non-identical Ikeda models and obtain existence conditions for the generalized synchronization. Numerical simulations fully support the analytical findings. Generalization of the approach to the wider class of non-linear chaotic systems is also presented.

Tracking control of nonlinear chaotic systems with dynamics uncertainties

This paper deals with the tracking control of nonlinear chaotic systems with dynamics uncertainties. A robust control strategy is developed to control a class of nonlinear chaotic systems with uncertainties. The proposed strategy is an input–output control scheme which comprises an uncertainty estimator and a linearizing-like feedback. The control time is explicitly computed. Computer simulations of the Duffing system are provided to verify the validity of the proposed control scheme.

Adaptive control and synchronization for a class of nonlinear chaotic systems using partial system states

Strategies to design adaptive controllers using only part of the system states for the stabilization of one chaotic system and the synchronization of two chaotic systems are proposed for a general class of chaotic systems. The transient performance in terms of the L 2 norm of system states is quantified as an explicit function of the design parameters so that designers can tune the design parameters in an explicit way to obtain the required closed loop behavior. Simulation results also verify the effectiveness of the proposed control schemes.

Generalized synchronization in time-delayed systems

We investigate the generalized synchronization between two unidirectionally linearly and nonlinearly coupled chaotic nonidentical Ikeda models and find existence conditions of the generalized synchronization. Also we study the chaos synchronization between nonidentical Ikeda models with variable feedback-delay times and find the existence and sufficient stability conditions for the retarded synchronization manifold with the coupling-delay lag time. Generalization of the approach to the wide class of nonlinear chaotic systems is also presented.

Global adaptive synchronization of chaotic systems with uncertain parameters

We propose a novel adaptive synchronization method for a class of nonlinear chaotic systems with uncertain parameters. Using the chaos control method, we derive a synchronizer, which can make the states of the driven system globally track the states of the drive system asymptotically. The advantage of our method is that our problem setting is more general than those that already exist and the synchronizer is simply constructed by an analytic formula, without knowledge in advance of the unknown bounds of the uncertain parameters. A computer simulation example is given to validate the proposed approach.