LMI-based fuzzy chaotic synchronization and communications

Addresses synthesis approaches for signal synchronization and secure communications of chaotic systems by using fuzzy system design methods based on linear matrix inequalities (LMIs). By introducing a fuzzy modeling methodology, many well-known continuous and discrete chaotic systems can be exactly represented by Takagi-Sugeno (T-S) fuzzy models with only one premise variable. Following the general form of fuzzy chaotic models, the structure of the response system is first proposed. Then, according to the applications of synchronization to the fuzzy models that have common bias terms or the same premise variable of drive and response systems, the driving signals are developed with four different types: fuzzy, character, crisp, and predictive driving signals. Synthesizing from the observer and controller points of view, all types of drive-response systems achieve asymptotic synchronization. For chaotic communications, the asymptotical recovering of messages is ensured by the same framework. It is found that many well-known chaotic systems can achieve their applications on asymptotical synchronization and recovering messages in secure communication by using either one type of driving signals or all. Several numerical simulations are shown with expected satisfactory performance     

时滞Chen混沌系统的指数同步及在保密通信中的应用

针对一类参数未知的时滞Chen混沌系统, 研究了其指数同步问题. 利用Lyapunov稳定理论设计了指数同步控制器和参数自适应律, 基于线性矩阵不等式技术给出了其指数同步的充分条件. 利用所提出的指数同步方法解决了保密通信问题, 且更符合实际情况. 所设计的控制器是实用有效, 易于实现. 仿真示例验证了该方法的有效性.     

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.     

混沌系统的一种新指数同步方法及其在保密通信中的应用*

为了探索出一种新的指数同步方法,在已有研究的基础上,将一种非线性系统的指数稳定定理与李亚谱诺夫稳定性定理相结合,设计出一种合理的非线性控制器,理论上严格分析了该方法的可行性。以超混沌Chen系统为例,利用该方法实现了两个超混沌Chen系统的指数同步,并且同步性能优越。同时,将该方法应用到保密通信中,仿真结果显示发送端的信号能在接收端很好地被恢复出来,从而表明了该方法的有效性且在保密通信中有一定的应用前景。     

Hybrid state-space fuzzy model-based controller with dual-ratesampling for digital control of chaotic systems

We develop a hybrid state-space fuzzy model-based controller with dual-rate sampling for digital control of chaotic systems. A Takagi-Sugeno (TS) fuzzy model is used to model the chaotic dynamic system and the extended parallel-distributed compensation technique is proposed and formulated for designing the fuzzy model-based controller under stability conditions. The optimal regional-pole assignment technique is also adopted in the design of the local feedback controllers for the multiple TS linear state-space models. The proposed design procedure is as follows: an equivalent fast-rate discrete-time state-space model of the continuous-time system is first constructed by using fuzzy inference systems. To obtain the continuous-time optimal state-feedback gains, the constructed discrete-time fuzzy system is then converted into a continuous-time system. The developed optimal continuous-time control law is finally converted into an equivalent slow-rate digital control law using the proposed intelligent digital redesign method. The main contribution of the paper is the development of a systematic and effective framework for fuzzy model-based controller design with dual-rate sampling for digital control of complex such as chaotic systems. The effectiveness and the feasibility of the proposed controller design method is demonstrated through numerical simulations on the chaotic Chua circuit     

Secure communications of chaotic systems with robust performancevia fuzzy observer-based design

This paper presents a systematic design methodology for fuzzy observer-based secure communications of chaotic systems with guaranteed robust performance. The Takagi-Sugeno fuzzy models are given to exactly represent chaotic systems. Then, the general fuzzy model of many well-known chaotic systems is constructed with only one premise variable in fuzzy rules and the same premise variable in the system output. Based on this general model, the fuzzy observer of chaotic system is given and leads the stability condition of a linear-matrix inequality problem. When taking the fuzzy observer-based design to applications on secure communications, the robust performance is presented by simultaneously considering the effects of parameter mismatch and external disturbances. Then, the error of the recovered message is stated in an H^∞ criterion. In addition, if the communication system is free of external disturbances, the asymptotic recovering of the message is obtained in the same framework. The main results also hold for applications on chaotic synchronization. Numerical simulations illustrate that this proposed scheme yields robust performance     

Intelligent fuzzy controller for chaos synchronization of uncertain fractional-order chaotic systems with input nonlinearities

In this research work, a novel fuzzy adaptive control is proposed to achieve a projective synchronization for a class of fractional-order chaotic systems with input nonlinearities (dead-zone together with sector nonlinearities). These master-slave systems under consideration are supposed to be with distinct models, different fractional-orders, unknown models, and dynamic external disturbances. The proposed control law consists of two main terms, namely: a fuzzy adaptive control term for appropriately approximating the uncertainties and a fractional-order variable-structure control term for robustly dealing with these inherent input nonlinearities. A Lyapunov approach is used to derive the updated laws and to prove the stability of the closed-loop control system. At last, a set of computer simulation results is carried out to illustrate and further validate the theoretical findings.     

Projective synchronization of two different fractional-order chaotic systems via adaptive fuzzy control

In this paper, the projective synchronization problem of two fractional-order different chaotic (or hyperchaotic) systems with both uncertain dynamics and external disturbances is considered. More particularly, a fuzzy adaptive control system is investigated for achieving an appropriate projective synchronization of unknown fractional-order chaotic systems. The adaptive fuzzy logic systems are used to approximate some uncertain nonlinear functions appearing in the system model. These latter are augmented by a robust control term to compensate for the unavoidable fuzzy approximation errors and external disturbances as well as residual error due to the use of the so-called e-modification in the adaptive laws. A Lyapunov approach is adopted for the design of the parameter adaptation laws and the proof of the corresponding stability as well as the asymptotic convergence of the underlying synchronization errors towards zero. The effectiveness of the proposed synchronization system is illustrated through numerical experiment results.     

Some synchronization criteria for bidirectionally-coupled chaotic systems

1IntroductionChaos synchronization,as a very important topic in thenonlinear science ,has been developed extensivelyinthelastfew years [1,2] .A wide variety of approaches [1 ~9]have been proposed for the synchronization of chaoticsystems which include linear and nonlinear feedback,adaptive control ,etc . Most of the methods mentionedabove synchronize two coupled identical chaotic systems .Accordingto the condition of coupling signal ,they can beclassified into bidirectional [3 ~5] and unidirec…     

Some synchronization criteria for bidirectionally-coupled chaotic systems

Based on the stability theory of linear time-varying continuous system,this paper investigates the synchronization of two linear bidirectionally-coupled systems.Sufficient conditions for asymptotic synchronization are obtained for general chaotic system with bidirectional coupling via linear error feedback.Since the trajectory of chaotic system is continuous and bounded,one can choose suitable coupled parameters to satisfy the proposed criterion.The criterion can also be applied to the global synchronization for chaotic systems with linear unidirectional coupling.The chaotic Chen system and the generalized Lorenz-like system are taken as examples,the simulations verify the effectiveness of the proposed method.     

Self-organizing adaptive fuzzy neural control for the synchronization of uncertain chaotic systems with random-varying parameters

This paper proposes a self-organizing adaptive fuzzy neural control (SAFNC) for the synchronization of uncertain chaotic systems with random-varying parameters. The proposed SAFNC system is composed of a computation controller and a robust controller. The computation controller containing a self-organizing fuzzy neural network (SOFNN) identifier is the principle controller. The SOFNN identifier is used to online estimate the compound uncertainties with the structure and parameter learning phases of fuzzy neural network (FNN), simultaneously. The structure-learning phase consists of the growing of membership functions, the splitting of fuzzy rules and the pruning of fuzzy rules, and thus the SOFNN identifier can avoid the time-consuming trial-and-error tuning procedure for determining the network structure of fuzzy neural network. The robust controller is used to attenuate the effects of the approximation error so that the synchronization of chaotic systems is achieved.All the parameter learning algorithms are derived based on the Lyapunov stability theorem to ensure network convergence as well as stable synchronization performance. To demonstrate the effectiveness of the proposed method, simulation results are illustrated in this paper.     

基于T-S模糊模型的混沌系统脉冲控制

给出了一种基于T-S模糊模型的混沌系统模糊脉冲控制方法.首先给出了基于T-S模糊模型对非线性系统精确建模的原理,得到与混沌系统等价的T-S模糊系统.然后根据建模得到的T-S模糊系统,采用模糊脉冲控制技术来实现控制.最后,以控制Ndolschi混沌系统为例,证明了这种方法的有效性.     

一类混沌系统的量化同步

针对信息受限的条件,研究了一类连续混沌系统的同步问题.通过一个有限容量的信道,将具有混沌形式的驱动系统和基于观测器的响应系统连接.在这种情况下,设计了有效的量化方法使得同步误差关于传输误差是输入状态稳定(ISS),同时保证传输误差是指数衰减的.从而使得混沌同步误差在信道容量有限条件下渐近趋于零.最后通过数值例子说明了本文方法的有效性.     

Reliable synchronization of nonlinear chaotic systems

This article addresses the reliable synchronization problem for a general class of chaotic systems. By combining the Lyapunov stability theory with the linear matrix inequality (LMI) optimization technique, a reliable feedback controller is established to guarantee synchronization between the master and slave chaotic systems even though some control component (actuator) failures occur. Finally, an illustrative example is provided to demonstrate the effectiveness of the results developed in this paper.     

非光滑系统的混沌同步

通过广义哈密顿系统和观测器法，本文将非光滑混沌系统的同步问题转化成了研究光滑系统零解的稳定性，从而给出了混沌同步的条件．对具体的带于摩擦，碰撞的Duffing振子分别进行研究，使其达到了完全同步，表明该方法的正确性．     

On feedback-controlled synchronization of chaotic systems

This paper studies a general setting of chaos synchronization in the form of a generalized Lur’e system, which includes both the classical and an earlier version of generalized Lur’e systems as special cases. More significantly, for this general setting, some fairly simple and easily used algebraic conditions are derived for verification and design of unidirectional feedback-controlled chaos synchronization. The Chen and Rössler systems are used as examples for illustration.     

混沌同步系统反馈系数的优化设计

为提高混沌同步系统抗信道噪声和元件参数失配干扰的能力，研究具有线性误差方程的一类连续变量反馈同步系统中反馈系数的优化设计问题。推导出反馈系数优化设计的目标函数和约束条件，用MATLAB软件对其进行优化设计。通过对蔡氏电路非线性反馈和线性反馈两种同步方案的仿真及实验表明，用该方法设计的混沌同步系统具有较强的抗干扰能力。     

Designing lag synchronization schemes for unified chaotic systems

Lag synchronization of chaotic unified systems is investigated theoretically and numerically. Three kinds of single-controller schemes are designed to achieve lag synchronization of the so-called chaotic unified systems and some results are proved theoretically using Lyapunov’s stability theory. Computer simulations are then provided to show the effectiveness and feasibility of the proposed methods.