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.     

Chaotic synchronization in the presence of disturbances based on an orthogonal function neural network

Chaos synchronization problems are addressed in this paper. For chaotic synchronization systems with uncertainties and external disturbances, an orthogonal function neural network is used to achieve the synchronization of chaotic systems. Legendre orthogonal polynomials are selected as the basis functions of the orthogonal function neural network. An adaptive learning law is derived to guarantee that the tracking errors are bounded using Lyapunov stability theory. Simulation results show the efficiency of the proposed scheme. Copyright © 2008 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society     

Control and synchronization of chaotic systems using a novel indirect model reference fuzzy controller

This paper presents a robust indirect model reference fuzzy control scheme for control and synchronization of chaotic nonlinear systems subject to uncertainties and external disturbances. The chaotic system with disturbance is modeled as a Takagi–Sugeno fuzzy system. Using a Lyapunov function, stable adaptation laws for the estimation of the parameters of the Takagi–Sugeno fuzzy model are derived as well as what the control signal should be to compensate for the uncertainties. The synchronization of chaotic systems is also considered in the paper. It is shown that by the use of an appropriate reference signal, it is possible to make the reference model follow the master chaotic system. Then, using the proposed model reference fuzzy controller, it is possible to force the slave to act as the reference system. In this way, the chaotic master and the slave systems are synchronized. It is shown that not only can the initial values of the master and the slave be different, but also there can be parametric differences between them. The proposed control scheme is simulated on the control and the synchronization of Duffing oscillators and Genesio–Tesi systems.     

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     

Observer-based hybrid adaptive fuzzy control for affine and nonaffine uncertain nonlinear systems

This paper presents a novel observer-based hybrid adaptive fuzzy controller for affine and nonaffine nonlinear systems with external disturbance. The suggested design is so easy and does not need a mathematical model for system under control and also it is very simple, efficient and robust. Based on the adaptive method and the system states observer, an observer-based adaptive fuzzy method is proposed to control an uncertain nonlinear system. Also, a supervisory controller term is employed to attenuate the residual error to a desired level and compensate the both uncertainties and observer errors. Although proposed control method needs the uncertainties to be bounded, it does not need this bound to be identified. Stability of the proposed method is shown based on Lyapunov theory and also the strictly positive real condition if all the implicated signals are uniformly bounded. Finally, in our simulation studies, to demonstrate the usefulness and efficiency of the suggested technique, an uncertain nonlinear system is employed.

     

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     

基于观测器的一类非线性系统的自适应模糊控制

针对一类有界的不确定非线性系统设计了模糊观测器和自适应控制器.该方法不需要系统状态完全可测的条件,而是通过模糊观测器估计系统的状态变量并且能保证观测误差是一致最终有界的.该自适应控制器取得了良好的控制效果并且保证了跟踪误差的一致最终有界性.仿真结果表明了本文所提出的方法有效性.     

Nonfragile asynchronous control for uncertain chaotic Lurie network systems with Bernoulli stochastic process

This paper proposes a novel nonfragile robust asynchronous control scheme for master‐slave uncertain chaotic Lurie network systems with randomly occurring time‐varying parameter uncertainties and controller gain fluctuation. The asynchronous phenomenon occurs between the system modes and the controller modes. In order to consider a more realistic situation in designing a reliable proportional‐derivative controller, Bernoulli stochastic process and memory feedback are introduced to the concept of nonlinear control system. First, by taking full advantage of the additional derivative state term and variable multiple integral terms, a newly augmented Lyapunov‐Krasovskii functional is constructed via an adjustable parameter. Second, based on new integral inequalities including almost all of the existing integral inequalities, which can produce more accurate bounds with more orthogonal polynomials considered, less conservative synchronization criteria are obtained. Third, a desired nonfragile estimator controller is achieved under the aforementioned methods. Finally, 4 numerical simulation examples of Chua's circuit and 3‐cell cellular neural network with multiscroll chaotic attractors are presented to illustrate the effectiveness and advantages of the proposed theoretical results.     

Exponential Lag Synchronization of Memristive Neural Networks with Reaction Diffusion Terms via Neural Activation Function Control and Fuzzy Model

This paper is concerned with the problem of exponential lag synchronization of memristive neural networks with reaction diffusion terms via neural activation function control and fuzzy model. An memristor‐based circuit which exhibits the feature of pinched hysteresis is introduced and further, the memristive neural networks with reaction diffusion terms and such system containing fuzzy model are described at length, respectively. By utilizing the Lyapunov functional method and the neural activation function controller depending on the output of the system in the case of packed circuits, some concise conditions are acquired to guarantee the slave systems exponential lag synchronized with the master systems. Finally, several simulated examples are also presented to demonstrate the correctness of the theoretical results.     

Non-monotonic robust H2 fuzzy observer-based control for discrete time nonlinear systems with parametric uncertainties

A non-monotonic Lyapunov function (NMLF) is deployed to design a robust H₂ fuzzy observer-based control problem for discrete-time nonlinear systems in the presence of parametric uncertainties. The uncertain nonlinear system is presented as a Takagi and Sugeno (T–S) fuzzy model with norm-bounded uncertainties. The states of the fuzzy system are estimated by a fuzzy observer and the control design is established based on a parallel distributed compensation scheme. In order to derive a sufficient condition to establish the global asymptotic stability of the proposed closed-loop fuzzy system, an NMLF is adopted and an upper bound on the quadratic cost function is provided. The existence of a robust H₂ fuzzy observer-based controller is expressed as a sufficient condition in the form of linear matrix inequalities (LMIs) and a sub-optimal fuzzy observer-based controller in the sense of cost bound minimization is obtained by utilising the aforementioned LMI optimisation techniques. Finally, the effectiveness of the proposed scheme is shown through an example.     

Interval type 2 hierarchical FNN with the H-infinity condition for MIMO non-affine systems

To develop a controller that deals with noise-corrupted training data and rule uncertainties for interconnected multi-input–multi-output (MIMO) non-affine nonlinear systems with unmeasured states, an interval type-2 fuzzy system is integrated with an observer-based hierarchical fuzzy neural controller (IT2HFNC) in this paper. Also, an H_∞ control technique and a strictly positive real Lyapunov (SPR-Lyapunov) design approach are employed for attenuating the influence of both external disturbances and fuzzy logic approximation error on the tracking of errors. Moreover, the proposed hierarchical fuzzy structure can greatly reduce the number of adjusted parameters of the IT2HFNC, and then, the problem of online computational burden can be solved. According to the design of the interval type-2 fuzzy neural network and H_∞ control technique, the IT2HFNN controller can improve its robustness to noise, uncertainties, approximation errors, and external disturbances. Simulation results are reported to show the performance of the proposed control system mode and algorithms.     

时滞混沌系统的同步与反同步及其在保密通信中的应用

根据Lyapunov稳定性理论结合线性矩阵不等式技巧,研究了一类时滞混沌神经网络的同步与反同步问题,设计了各自的状态反馈控制器,并从理论上实现了此类时滞混沌系统的同步与反同步。最后将此类混沌系统应用于保密通信,通过同步与反同步系统的切换,设计出具体的数字保密通信方案,数值仿真验证了该方法的有效性。     

Fixed-time synchronization of neural networks with time delay via quantized intermittent control

This paper presents an approach for fixed-time synchronization (FIXTS) of neural networks (NNs) by designing quantized intermittent controller. Under the intermittent controller, the synchronization between neural network systems with time delay can be realized. Based on intermittent strategy, FIXTs theory is proposed, and a sufficient condition is established to realize the FIXTS of the master–slave NNs. At the same time, the establishment time of FIXTS is estimated. Finally, the simulation of Gilli attractor to prove the validity of the proposed method.     

Robust approximation‐based adaptive control of multiple state delayed nonlinear systems with unmodeled dynamics

This paper addresses the problem of tracking control for a class of uncertain nonstrict‐feedback nonlinear systems subject to multiple state time‐varying delays and unmodeled dynamics. To overcome the design difficulty in system dynamical uncertainties, radial basis function neural networks are employed to approximate the black‐box functions. Novel continuous functions that deal with whole states uncertainties are introduced in each step of the adaptive backstepping to make the controller design feasible. The robust problem caused by unmodeled dynamics when constructing a stable controller is solved by employing an auxiliary signal to regulate its boundedness. A novel Lyapunov‐Krasovskii functional is developed to compensate for the delayed nonlinearity without requiring the priori knowledge of its upper bound functions. On the basis of the proposed robust adaptive neural controller, all the closed‐loop signals are semiglobal uniformly ultimately bounded with good tracking performance.     

Coordination control for bilateral teleoperation with kinematics and dynamics uncertainties

The coordination control design problem for the master–slave system is addressed in this paper. In order to meet the actual work condition, we assume that the master works in a laboratory, the slave works in remote side where the environment is very complex, and the master and slave are in different sizes. Three problems are needed to be solved: system dynamics uncertainties, system kinematics uncertainties, and the asymmetric time-varying delays. The new task-space based Proporation plus damping (P+d) controller and adaptive fuzzy P+d controller are proposed for the master and the slave, respectively. By choosing proper Lyapunov functions, we have proved that the synchronization errors converge to zero asymptotically with the new controllers. The delay-dependent stability criterion is derived. With the given parameters, the proposed allowable maximal transmission delay can be computed. Finally, the simulations are performed to show the effectiveness of the proposed method.     

Exponential Synchronization of Stochastic Fuzzy Cellular Neural Networks with Reaction-Diffusion Terms via Periodically Intermittent Control

This paper considers the exponential synchronization of stochastic fuzzy cellular neural networks with time-varying delays and reaction-diffusion terms based on p-norm. Motivated by the achievements from both the stability of fuzzy cellular neural networks with stochastic perturbation and reaction-diffusion effects and the synchronization issue of coupled chaotic delayed neural networks by using periodically intermittent control approach, a periodically intermittent controller is proposed to guarantee the exponential synchronization of the coupled chaotic neural networks by using Lyapunov stability theory and stochastic analysis approaches. The synchronization results presented in this paper generalize and improve many known results. This paper also presents an illustrative example and uses simulated results of this example to show the feasibility and effectiveness of the proposed scheme.     

控制方向未知的不确定系统预设性能自适应神经网络反演控制

对一类控制方向未知的不确定严格反馈非线性系统的预设性能自适应神经网络反演控制问题进行了研究.系统中含有时变非匹配不确定项且控制方向未知.首先,提出了一种新的误差转化方法,放宽了对初始误差已知的限制;随后,利用径向基函数(radial basis function,RBF)神经网络及跟踪微分器分别实现了对未知函数和虚拟控制量导数的逼近,并综合运用Nussbaum函数和反演控制技术设计了控制器.所设计的控制器能保证系统内所有信号有界且输出误差满足预设的瞬态和稳态性能要求.最后的仿真研究验证了控制器设计方法的有效性.     

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Ikeda系统同步及其在保密通信中的应用

针对一类时滞Ikeda混沌系统,利用Lyapunov稳定和微分不等式,研究了其指数同步问题。基于线性矩阵不等式理论得到了指数同步的充分条件,给出了指数同步控制器的设计方法,利用混沌掩盖将该同步方法应用于保密通信。仿真表明,该方案具有同步速度快、鲁棒性良好等优良性能。     

时变时滞非线性系统的间歇控制

时变时滞广泛存在于各种非线性系统中,研究了时变时滞非线性系统的间歇控制及其在保密通信中的应用问题,提出了一种间歇控制策略,理论上分析了其正确性,并且给出一个定理来确定控制器的相关参数。根据提出的定理,设计出间歇控制器使得两个含有时变时滞的Chua电路指数达到同步。将该方法应用到混沌保密通信中,在两个系统达到同步的基础上,发送端的信号能够在接收端很好地恢复出来,表明了该方法的可行性。