Synchronization Of Uncertain Chaotic Systems Research Articles

Quadratic optimal neural fuzzy control for synchronization of uncertain chaotic systems

This paper presents a novel quadratic optimal neural fuzzy control for synchronization of uncertain chaotic systems via H ∞ approach. In the proposed algorithm, a self-constructing neural fuzzy network (SCNFN) is developed with both structure and parameter learning phases, so that the number of fuzzy rules and network parameters can be adaptively determined. Based on the SCNFN, an uncertainty observer is first introduced to watch compound system uncertainties. Subsequently, an optimal NFN-based controller is designed to overcome the effects of unstructured uncertainty and approximation error by integrating the NFN identifier, linear optimal control and H ∞ approach as a whole. The adaptive tuning laws of network parameters are derived in the sense of quadratic stability technique and Lyapunov synthesis approach to ensure the network convergence and H ∞ synchronization performance. The merits of the proposed control scheme are not only that the conservative estimation of NFN approximation error bound is avoided but also that a suitable-sized neural structure is found to sufficiently approximate the system uncertainties. Simulation results are provided to verify the effectiveness and robustness of the proposed control method.

Fuzzy model based adaptive synchronization of uncertain chaotic systems: Robust tracking control approach

This Letter presents fuzzy model-based robust tracking control for the adaptive synchronization of uncertain chaotic systems. Fuzzy model and adaptive algorithm are employed to present the unknown chaotic systems. H ∞ and sliding mode control are combined to construct a robust tracking controller. The incorporated H ∞ controller can attenuate the external disturbance and approximation error to any prescribed level. The proposed scheme guarantees that all the variables are bounded and the tracking error is compensated.

OBSERVER-BASED SYNCHRONIZATION OF UNCERTAIN CHAOTIC SYSTEMS: COMPARISON BETWEEN REDUCED-ORDER AND FULL-ORDER OBSERVERS

Within the drive-response configuration, this paper considers the synchronization of uncertain chaotic systems based on observers. Even if there are unknown disturbances and parameters in the drive system, a robust adaptive full-order observer can be used to realize chaos synchronization. Further, we develop a reduced-order observer-based response system to synchronize the drive system. By choosing a special reduced-order gain matrix, the reduced-order observer-based response system turns out to be linear and can eliminate the influence of the unknown disturbances and parameters directly. We also discuss the above mentioned two kinds of observers in numerical simulation, and demonstrate that the linear reduced-order observer-based response system is better than the full-order observer-based one.

Fuzzy adaptive synchronization of uncertain chaotic systems via delayed feedback control

Based on the T–S fuzzy model and the delayed feedback control (DFC) scheme, this Letter presents a robust synchronization strategy for a class of chaotic system with unknown parameters and disturbances. Being the response system, the designed robust observer can adaptively track the drive system globally. The T–S fuzzy model of the 4D chaotic system (Lorenz–Stenflo) is developed as an example for illustration. Numerical simulations are shown to verify the results.

Observer-based synchronization of uncertain chaotic system and its application to secure communications

Within the drive-response configuration, this paper considers the synchronization of uncertain chaotic systems based on observers and chaos-based secure communication. Even if there are unknown disturbances and parameters in the drive system, a robust adaptive observer can be used as response system to realize chaotic synchronization. The proposed method is then applied to secure communication. The transmitter is constructed by injecting the information into the drive system with proper manner and one of the transmitting signal is the sum of one of the output and the information signal. The Lur’e chaotic system is considered as an illustrative example to demonstrate the effectiveness of the proposed approaches.

Backstepping synchronization of uncertain chaotic systems by a single driving variable

In this paper a parameter observer and a synchronization controller are designed to synchronize unknown chaotic systems with diverse structures. Based on stability theory the structures of the observer and the controller are presented. The unknown Coullet system and Rossler system are taken for examples to demonstrate that the method is effective and feasible. The artificial simulation results show that global synchronization between the unknown Coullet system and the Rossler system can be achieved by a single driving variable with co-operation of the observer and the controller, and all parameters of the Coullet system can be identified at the same time.

Robust adaptive neural-fuzzy-network control for the synchronization of uncertain chaotic systems

This paper proposes a robust adaptive neural-fuzzy-network control (RANFC) to address the problem of controlled synchronization of a class of uncertain chaotic systems. The proposed RANFC system is comprised of a four-layer neural-fuzzy-network (NFN) identifier and a supervisory controller. The NFN identifier is the principal controller utilized for online estimation of the compound uncertainties. The supervisory controller is used to attenuate the effects of the approximation error so that the perfect tracking and synchronization of chaotic systems are achieved. All the parameter learning algorithms are derived based on Lyapunov stability theorem to ensure network convergence as well as stable synchronization performance. Finally, simulation results are provided to verify the effectiveness and robustness of the proposed RANFC methodology.

Adaptive Synchronization of Uncertain Chaotic Systems Based on T–S Fuzzy Model

This paper presents an adaptive approach for synchronization of Takagi-Sugeno (T-S) fuzzy chaotic systems. T-S fuzzy model can represent a general class of nonlinear system and we employ it for fuzzy modeling of the chaotic drive system. Since the output of the drive system is only available for synchronization, the response system is designed based on fuzzy adaptive observer for uncertain parameters and parameter mismatch cases. We analyze the stability of the overall fuzzy synchronization system by applying Lyapunov stability theory and derive stability conditions by solving linear matrix inequalities (LMIs) problem. The adaptive law is derived to estimate the uncertain parameters or parameter mismatch. Numerical examples are given to demonstrate the validity of the proposed fuzzy adaptive synchronization approach.

Synchronization of uncertain chaotic systems using a single transmission channel

This paper proposes a robust sliding mode observer for synchronization of uncertain chaotic systems with multi-nonlinearities. A new control strategy is proposed for the construction of the robust sliding mode observer, which can avoid the strict conditions in the design process of Walcott-Żak observer. A new method of multi-dimensional signal transmission via single transmission channel is proposed and applied to chaos synchronization of uncertain chaotic systems with multi-nonlinearities. The simulation results are presented to validate the method.

LMI criteria for robust chaos synchronization of a class of chaotic systems

Based on the Lyapunov stability theory and LMI technique, a new sufficient criterion, formulated in the LMI form, is established in this paper for chaos robust synchronization by linear-state-feedback approach for a class of uncertain chaotic systems with different parameters perturbation and different external disturbances on both master system and slave system. The new sufficient criterion can guarantee that the slave system will robustly synchronize to the master system at an exponential convergence rate. Meanwhile, we also provide a criterion to find out proper feedback gain matrix K that is still a pending problem in literature [H. Zhang, X.K. Ma, Synchronization of uncertain chaotic systems with parameters perturbation via active control, Chaos, Solitons and Fractals 21 (2004) 39–47]. Finally, the effectiveness of the two criteria proposed herein is verified and illustrated by the chaotic Murali–Lakshmanan–Chua system and Lorenz systems, respectively.

On the synchronization of uncertain chaotic systems

In this article, we investigate the synchronization of uncertain chaotic systems. Based upon the parameters identification technique and a simple but efficient control method, we control the response system to be the drive system with parameters unknown. The techniques are successfully applied to Lorenz system and Chen system. Furthermore, the effect of external noise is under our discussion.

Synchronization of uncertain chaotic systems with perturbation based on variable structure control

Synchronization of uncertain nonlinear chaotic systems with perturbation based on variable structure control is investigated. The controller is designed directly for nonlinear system via appropriate switching surface selection such that the system state reaches it in finite time. The estimation of the bounds on system uncertainties and disturbances is given. The proposed controller has strong robustness with respect to perturbation. Simulation results are proposed to demonstrate the effectiveness of the method.

Reduced-order synchronization of chaotic systems with parameters unknown

In this Letter, we investigate the reduced-order synchronization of uncertain chaotic systems. Based upon the parameters modulation and the adaptive control techniques, we control the response system to be the drive system even though their orders are different and their parameters are unknown. The techniques are successfully applied to two examples: generalized Lorenz system (fourth order) and Lü system (third order); Rössler hyperchaotic system (fourth order) and Rössler system (third order). Furthermore, the effect of control modulator k is under our discussions.

Reduced-order synchronization of uncertain chaotic systems via adaptive control

We consider the coupling of two uncertain dynamical systems with different orders using an adaptive feedback linearization controller to achieve reduced-order synchronization between the two systems. Reduced-order synchronization is the problem of synchronization of a slave system with projection of a master system. The synchronization scheme is an exponential linearizing-like controller and a state/uncertainty estimator. As an illustrative example, we show that the dynamical evolution of a second-order driven oscillator can be synchronized with the canonical projection of a fourth-order chaotic system. Simulation results indicated that the proposed control scheme can significantly improve the synchronousness performance. These promising results justify the usefulness of the proposed output feedback controller in the application of secure communication.

Fuzzy adaptive synchronization of uncertain chaotic systems

This Letter presents an adaptive approach for synchronization of Takagi–Sugeno (T–S) fuzzy chaotic systems. Since the parameters of chaotic system are assumed unknown, the adaptive law is derived to estimate the unknown parameters and its stability is guaranteed by Lyapunov stability theory. The control law to be designed consists of two parts: one part that can stabilize the synchronization error dynamics and the other part that estimates the unknown parameters. Numerical examples are given to demonstrate the validity of the proposed adaptive synchronization approach.

Synchronization of uncertain chaotic systems via backstepping approach

In this paper, adaptive synchronization of two uncertain chaotic systems is presented using adaptive backstepping approach. The master system is any smooth nonlinear chaotic system, while the slave system is a nonlinear chaotic system in the feedback form. Global stability and exponential synchronization between the master and slave systems can be achieved. The proposed approach offers a systematic design procedure for adaptive synchronization of a large class of continuous-time chaotic systems in the chaos research literature. Computer simulations are provided to verify the operation of the designed synchronization scheme.

Adaptive backstepping synchronization of uncertain chaotic system

In this paper, an adaptive backstepping design is proposed to synchronize two uncertain chaos systems. This method can be applied to a variety of chaos systems which can be transformed into the so-called general strict-feedback form no matter whether it contains external excitation or not. Rössler system and Duffing oscillator are used as examples for detailed description. Numerical simulations show the effectiveness and feasibility of the method.

Adaptive synchronization of uncertain chaotic systems via backstepping design

In this paper, an approach for adaptive synchronization of uncertain chaotic systems is proposed using adaptive backstepping with tuning functions. Strong properties of global stability and asymptotic synchronization can be achieved. The proposed approach offers a systematic design procedure for adaptive synchronization of a large class of continuous-time chaotic systems in the chaos research literature. Simulation results are presented to show the effectiveness of the approach.