On impulsive control for synchronization and its application to the nuclear spin generator system

The issue of impulsive control theory for the synchronization of the nuclear spin generator (NSG) chaotic systems is developed. We propose an impulsive control scheme for the complete synchronization of the NSG system including chaotic systems. A sufficient condition for the impulsive control is derived, with an easily calculated maximum impulsive interval. The proposed impulsive control scheme is applied to the NSG system and the simulation result demonstrates the effectiveness of the method.     

Adaptive‐impulsive function projective synchronization for a class of time‐delay chaotic systems

This article investigates the function projective synchronization (FPS) for a class of time‐delay chaotic system via nonlinear adaptive‐impulsive control. To achieve the FPS, suitable nonlinear continuous and impulsive controllers are designed based on adaptive control theory and impulsive control theory. Using the generalized Babarlat's lemma, a general condition is given to ensure the FPS. Here, the time‐delay chaotic system is assumed to satisfy the Lipschitz condition while the Lipschitz constants are estimated by augmented adaptation equations. Numerical simulation results are also presented to verify the effectiveness of the proposed synchronization scheme. © 2014 Wiley Periodicals, Inc. Complexity 21: 333–341, 2015     

Sector-condition-based results for adaptive control and synchronization of chaotic systems under input saturation

This paper addresses the design of adaptive feedback controllers for two problems (namely, stabilization and synchronization) of chaotic systems with unknown parameters by considering input saturation constraints. A novel generalized sector condition is developed to deal with the saturation nonlinearities for synthesizing the nonlinear and the adaptive controllers for the stabilization and synchronization control objectives. By application of the proposed sector condition and rigorous regional stability analysis, control and adaptation laws are formulated to guarantee local stabilization of a nonlinear system under actuator saturation. Further, simple control and adaptation laws are developed to synchronize two chaotic systems under uncertain parameters and input saturation nonlinearity. Numerical simulation results for Rössler and FitzHugh–Nagumo models are provided to demonstrate the effectiveness of the proposed adaptive stabilization and synchronization control methodologies.     

Dynamical behaviors of a new hyperchaotic system

Currently, chaotic systems and chaos‐based applications are commonly used in the engineering fields. One of the main structures used in these applications is chaotic control and synchronization. In this paper, the dynamical behaviors of a new hyperchaotic system are considered. Based on Lyapunov Theorem with differential and integral inequalities, the global exponential attractive sets and positively invariant sets are obtained. Furthermore, the rate of the trajectories is also obtained. The global exponential attractive sets of the system obtained in this paper also offer theoretical support to study chaotic control, chaotic synchronization for this system. Computer simulation results show that the proposed method is effective. Copyright © 2014 John Wiley & Sons, Ltd.     

Generalized synchronization of continuous chaotic system

Sufficient condition for the generalized synchronization of continuous chaotic system with a kind of nonlinear transformation is derived. The method is illustrated by applications to Lorenz and Duffing chaotic systems and the simulation results demonstrate the effectiveness of the proposed theorem.     

基于T-S模型的Lurie混沌系统的模糊控制

针对Lurie混沌控制系统,进行了T-S模糊建模和模糊控制器设计,从而实现了Lurie混沌系统的稳定.在用T-S模糊模型精确重构Lurie系统结构的基础上,利用反馈同步思想,基于并行分布补偿(PDC)技术,得到了简单且易实现的控制器.仿真结果验证了该控制方法的有效性.     

一类统一混沌系统的追踪控制与同步

对一类统一混沌系统进行控制，设计出一种含参控制器，使受控系统追踪任意给定的一维参考信号和三维参考信号，利用Lyapunov方法证明在此控制器作用下该系统按指数速率收敛到参考信号。同时研究了此受控统一混沌系统的自同步及异结构同步问题。利用Chen′s混沌系统进行数值仿真，其结果说明了此控制器设计方法的有效性。     

Quadratic optimal synchronization of uncertain chaotic systems

This paper investigates the quadratic optimal synchronization of uncertain chaotic systems with parameter mismatch, parametric perturbations and external disturbances on both master and slave systems. A robust control scheme based on Lyapunov stability theory and quadratic optimal control approach is derived to realize chaotic synchronization. The sufficient criterion for stability condition is formulated in a linear matrix inequality (LMI) form. The effect of uncertain parameters and external disturbance is suppressed to an H_∞ norm constraint. An adaptive algorithm is proposed to adjust the uncertain bound in the robust controller avoiding the chattering phenomena. The simulation results for synchronization of the Chua’s circuit system and the Lorenz system demonstrate the effectiveness of the proposed scheme.     

Chaos synchronization and chaos control of quantum-CNN chaotic system by variable structure control and impulse control

In this paper, we derive some less stringent conditions for the exponential and asymptotic stability of impulsive control systems with impulses at fixed times. These conditions are then used to design an impulsive control law for the Quantum Cellular Neural Network chaotic system, which drives the chaotic state to zero equilibrium and synchronizes two chaotic systems. An active sliding mode control method is synchronizing two chaotic systems and controlling chaotic state to periodic motion state. And a sufficient condition is drawn for the robust stability of the error dynamics, and is applied to guiding the design of the controllers. Finally, numerical results are used to show the robustness and effectiveness of the proposed control strategy.     

Design of LMI‐based global sliding mode controller for uncertain nonlinear systems with application to Genesio's chaotic system

Design of a novel global sliding mode control law for the stabilization of uncertain nonlinear systems is presented in this article. A sufficient condition is derived using the Lyapunov theorem and linear matrix inequality to guarantee the asymptotical stability of the states and to improve the stability of the system. Under the uncertainty and nonlinearity effects, the reaching phase is eliminated and the chattering is reduced effectively and then, the robustness and performance of the system are improved. Lastly, the proposed method is applied on Genesio's chaotic system and the simulation results demonstrate the effectiveness of this technique. © 2014 Wiley Periodicals, Inc. Complexity 21: 94–98, 2015     

Control uncertain Genesio–Tesi chaotic system: Adaptive sliding mode approach

An adaptive sliding mode control (ASMC) technique is introduced in this paper for a chaotic dynamical system (Genesio–Tesi system). Using the sliding mode control technique, a sliding surface is determined and the control law is established. An adaptive sliding mode control law is derived to make the states of the Genesio–Tesi system asymptotically track and regulate the desired state. The designed control scheme can control the uncertain chaotic behaviors to a desired state without oscillating very fast and guarantee the property of asymptotical stability. An illustrative simulation result is given to demonstrate the effectiveness of the proposed adaptive sliding mode control design.     

一类非线性混沌系统混沌吸引子的冲击控制

在国内外研究工作的基础上,给出了一类非线性混沌系统混沌吸引子的冲击控制方案,运用普适方程的冲击控制理论导出了这类混沌系统混沌吸引子的冲击控制渐进稳定的条件,利用这一条件给出了混沌吸引子渐进稳定冲击控制的区间上界,最后给出了许多数据结果,这些结果对于混沌吸引子的控制将有重要的参考价值．     

Fast synchronization of non-identical chaotic modulation-based secure systems using a modified sliding mode controller

In this paper, a secure communication scheme based on chaotic modulation is proposed using a reversible process and a robust controller with efficient cost and complexity to synchronize two different chaotic systems. In the controller design, a sliding mode control with an adaptive rule is used for non-linear inputs. The adaptive rule is applied to ensure the synchronization when uncertainties, non-modeled dynamics or external distortions are at work. The message signal is recovered at the receiver using a recursive process at the end. The effectiveness of the proposed algorithm is confirmed via the simulation results for the synchronization of the transmitted signal modulated by Chen chaotic system at the transmitter and Genesio chaotic system at the receiver, and those for the information recovery process.     

Analysis of Topological Structure in Transiently Chaotic Neural Networks

Under the condition that the damping factor is between zero and one, chaotic dynamics is proved to exist in one-dimensional transiently chaotic neural networks by Li-Misiurewicz theorem. This result extends the previous result which is done under the condition that the damping factor is zero. Because the value of damping factor affects the speed of dynamical process of transiently chaotic neural networks, this result provides more complete theoretical basis for applications. Finally, two examples by numerical simulation are given to reinforce and illustrate this result.     

Minimum entropy control of chaos via online particle swarm optimization method

One of the recently developed approaches for control of chaos is the minimum entropy (ME) control technique. In this method an entropy function based on the Shannon definition, is defined for a chaotic system. The control action is designed such that the entropy as a cost function is minimized which results in more regular pattern of motion for the system trajectories. In this paper an online optimization technique using particle swarm optimization (PSO) method is developed to calculate the control action based on ME strategy. The method is examined on some standard chaotic maps with error feedback and delayed feedback forms. Considering the fact that the optimization is online, simulation results show very good effectiveness of the presented technique in controlling chaos.     

Controlling chaos based on an adaptive adjustment mechanism

In this paper, we extend the ideas and techniques developed by Huang [Huang W. Stabilizing nonlinear dynamical systems by an adaptive adjustment mechanism. Phys Rev E 2000;61:R1012–5] for controlling discrete-time chaotic system using adaptive adjustment mechanism to continuous-time chaotic system. Two control approaches, namely adaptive adjustment mechanism (AAM) and modified adaptive adjustment mechanism (MAAM), are investigated. In both case sufficient conditions for the stabilization of chaotic systems are given analytically. The simulation results on Chen chaotic system have verified the effectiveness of the proposed techniques.     

Controlling chaos based on an adaptive adjustment mechanism

In this paper, we extend the ideas and techniques developed by Huang [Huang W. Stabilizing nonlinear dynamical systems by an adaptive adjustment mechanism. Phys Rev E 2000;61:R1012–5] for controlling discrete-time chaotic system using adaptive adjustment mechanism to continuous-time chaotic system. Two control approaches, namely adaptive adjustment mechanism (AAM) and modified adaptive adjustment mechanism (MAAM), are investigated. In both case sufficient conditions for the stabilization of chaotic systems are given analytically. The simulation results on Chen chaotic system have verified the effectiveness of the proposed techniques.     

Robust adaptive neural network synchronization controller design for a class of time delay uncertain chaotic systems

In this paper, a robust adaptive neural network synchronization controller is proposed for two chaotic systems with input time delay and uncertainty. The studied chaotic system may possess a wide class of nonlinear time-delayed input uncertainty. The radial basis function (RBF) neural network is used to approximate the unknown continuous bounded function item of the time delay uncertainty via appropriate weight value updated law. With the output of RBF neural network, a robust adaptive synchronization control scheme is presented for the time delay uncertain chaotic system. Finally, a simulation example is used to illustrate the effectiveness of the proposed synchronization control scheme.     

Adaptive control of discrete-time chaotic systems: a fuzzy control approach

This paper discusses adaptive control of a class of discrete-time chaotic systems from a fuzzy control approach. Using the T–S model of discrete-time chaotic systems, an adaptive control algorithm is developed based on some conventional adaptive control techniques. The resulting adaptively controlled chaotic system is shown to be globally stable, and its robustness is discussed. A simulation example of the chaotic Henon map control is finally presented, to illustrate an application and the performance of the proposed control algorithm.