A Nussbaum gain adaptive synchronization of a new hyperchaotic system with input uncertainties and unknown parameters

The sign of unknown input coefficients is assumed to be known in most papers about the input uncertainties. In this paper, a Nussbaum gain method is adopted to cope with the situation that both the sign and the value of input are unknown. And the unknown parameters can be estimated under the situation of unknown sign of control. The synchronization is achieved for a class of hyperchaotic systems with unknown parameters and input uncertainties by adopting of the Nussbaum gain method and the global terminal adaptive method. And the conclusions are made as follows: First, the proposed method is effective in the situation that the sign of input is unknown. Second, the estimation of unknown parameters can be achieved only when the number of unknown parameters satisfied some condition and no uncertainty exist in the input of systems. Third, the unknown parameters cannot be estimated correctly with common adaptive method when there are input uncertainties in the system. But the Nussbaum gain method can get good result in the estimation of unknown parameters. At last, numerical simulations are done to show the effectiveness of the proposed method.     

带Gauss型误差的GMANOVA-MANOVA模型中未知参数的精确置信域

对于带Gauss型误差的GMANOVA-MANOVA模型,在均匀协方差结构下,求出了其中未知参数的极大似然估计及其均值和方差,并依据极大似然估计构造了未知参数的精确置信域.     

Synchronization of two different uncertain chaotic systems with unknown parameters using a robust adaptive sliding mode controller

In this paper, a robust adaptive sliding mode controller (RASMC) is proposed to realize chaos synchronization between two different chaotic systems with uncertainties, external disturbances and fully unknown parameters. It is assumed that both master and slave chaotic systems are perturbed by uncertainties, external disturbances and unknown parameters. The bounds of the uncertainties and external disturbances are assumed to be unknown in advance. Suitable update laws are designed to tackle the uncertainties, external disturbances and unknown parameters. For constructing the RASMC a simple sliding surface is first designed. Then, the RASMC is derived to guarantee the occurrence of the sliding motion. The robustness and stability of the proposed RASMC is proved using Lyapunov stability theory. Finally, the introduced RASMC is applied to achieve chaos synchronization between three different pairs of the chaotic systems (Lorenz–Chen, Chen–Lorenz, and Liu–Lorenz) in the presence of the uncertainties, external disturbances and unknown parameters. Some numerical simulations are given to demonstrate the robustness and efficiency of the proposed RASMC.     

Adaptive modified function projective synchronization of hyperchaotic systems with unknown parameters

This paper is involved with the adaptive modified function projective synchronization (MFPS) problem of hyperchaotic systems with unknown parameters. Based on the Lyapunov stability theorem and adaptive control method, adaptive controllers and parameters update laws can be presented for the MFPS not only between two identical hyperchaotic systems but particularly also between two different hyperchaotic systems with fully unknown or partially unknown parameters. Moreover, the coupling strength can be automatically adapted to a updated law. Numerical simulations are presented to show the effectiveness of the proposed synchronization schemes.     

Recovering unknown model parameters contained in a class of time-variant chaotic dynamical systems

This work deals mainly with the problem of recovering all unknown parameters for a class of time-variant chaotic dynamical systems from given time sequence. Based on synchronization between a chaotic sender system and an additional receiver system, a procedure, which combines a linear feedback technique with updated feedback gain and an adapted control strategy associated with the law of estimated parameters, is developed to dynamically determine the values of unknown parameters contained in the sender system. To promote widespread applications, the structure of the receiver system can be independent of that of the sender system. The effectiveness of this procedure is guaranteed by the periodic version of the classical LaSalle invariance principle of differential equations. Illustrations are presented for a harmonically excited Duffing oscillator and a four dimensional chaotic oscillator. The numerical results reveal the present procedure not only can precisely recover unknown model parameters, but also can rapidly response to sudden changes in unknown parameters. In addition, it has great robustness against the disturbance of noise.     

Adaptive control and synchronization of a coupled dynamo system with uncertain parameters

This paper treats the adaptive control and synchronization of the coupled dynamo system with unknown parameters. Based on the Lyapunov stability technique, an adaptive control laws are derived such that the coupled dynamo system is asymptotically stable and the two identical dynamo systems are asymptotically synchronized. Also the update rules of the unknown parameters are derived. Finally, numerical simulation of the controlled and synchronized systems are presented.     

Adaptive control and synchronization of a four-dimensional energy resources system with unknown parameters

This paper is involved with control and synchronization of a new four-dimensional energy resources system with unknown parameters. Based on the Lyapunov stability theorem, by designed adaptive controllers and parameter update laws, this system is stabilized to unstable equilibrium and synchronizations between two systems with different unknown system parameters are realized Numerical simulations are given for the purpose of illustration and verification.     

Adaptive synchronization of T–S fuzzy chaotic systems with unknown parameters

This paper presents a fuzzy model-based adaptive approach for synchronization of chaotic systems which consist of the drive and response systems. Takagi–Sugeno (T–S) fuzzy model is employed to represent the chaotic drive and response systems. Since the parameters of the drive system are assumed unknown, we design the response system that estimates the parameters of the drive system by adaptive strategy. The adaptive law is derived to estimate the unknown parameters and its stability is guaranteed by Lyapunov stability theory. In addition, the controller in the response system contains two parts: one part that can stabilize the synchronization error dynamics and the other part that estimates the unknown parameters. Numerical examples, including Duffing oscillator and Lorenz attractor, are given to demonstrate the validity of the proposed adaptive synchronization approach.     

Admissibility of Confidence Estimators in the Regression Model

In the regression model, we assume that the independent variables are random instead of fixed. Consider the problem of estimating the coverage function of a usual confidence interval for the unknown intercept parameter. In this paper, we consider a case in which the number of unknown parameters is smaller than 5. We show that the usual constant coverage probability estimator is admissible in the usual sense in this case. Note that this estimator is inadmissible in the usual sense in the other case where the number of unknown parameters is greater than 4.     

Asymptotically optimal estimation in a linear-fractional regression problem with random errors in coefficients

Considering the linear-fractional regression problem with errors in independent variables, we construct and study asymptotically optimal estimators for unknown parameters in the case of violation of the classical regression assumptions (the variances of the observations are different and depend on the unknown parameters).     

Synchronization of two hyperchaotic systems via adaptive control

This letter presents chaos synchronization problem of two different hyperchaotic systems when the parameters of drive and response systems are fully unknown or uncertain. Based on Lyapunov stability theory, an adaptive control law and a parameter update rule for unknown parameters are derived such that two different high dimensional chaotic systems are to be synchronized. Hyperchaotic Chen system and Second-harmonic generation (SHG) system are taken as an illustrative example to show the effectiveness of the proposed method.     

Adaptive synchronization of a hyperchaotic system with uncertain parameter

This paper addresses the synchronization problem of two Lü hyperchaotic dynamical systems in the presence of unknown system parameters. Based on Lyapunov stability theory an adaptive control law is derived to make the states of two identical Lü hyperchaotic systems with unknown system parameters asymptotically synchronized. Numerical simulations are presented to show the effectiveness of the proposed chaos synchronization schemes.     

多变量非线性贝叶斯动态模型的参数估计

本文讨论多变量非线性贝叶斯动态模型参数估计 ,将 Monte Carlo最优法用于极大似然函数 ,得到未知参数和状态变量的估计     

应力为SGBVE分布强度为指数分布下结构可靠度的估计

考虑了应力服从SGBVE分布,强度服从指数分布的应力—强度模型,分别在应力参数未知和部分强度参数未知的情形下给出了该模型可靠度的估计,并讨论了其性质.     

受扰不确定混沌系统的双路组合函数投影同步

研究了具有未知参数和外界扰动的多个混沌系统之间的双路组合函数投影同步问题.首先给出了由四个混沌驱动系统和两个混沌响应系统组成的双路组合函数投影同步系统的定义,然后以Lyapunov稳定性理论和不等式变换方法为分析依据,设计了鲁棒自适应控制器和参数自适应律,使得两路同步系统中的响应系统和驱动系统按照相应的函数比例因子矩阵实现同步,并有效克服未知有界干扰和未知参数的影响.相应的理论分析和数值仿真证明了该同步方案的可行性和有效性.     

Nonparametric estimation of the location and scale parameters based on density estimation

Summary By representing the location and scale parameters of an absolutely continuous distribution as functionals of the usually unknown probability density function, it is possible to provide estimates of these parameters in terms of estimates of the unknown functionals. Using the properties of well-known methods of density estimates, it is shown that the proposed estimates possess nice large sample properties and it is indicated that they are also robust against dependence in the sample. The estimates perform well against other estimates of location and scale parameters.     

应力为MOBVE分布强度为指数分布下串联结构可靠度的估计

考虑了应力服从MOBVE分布,强度服从指数分布的应力——强度模型,分别在应力参数未知和强度参数未知情形下给出了该模型在串联系统下可靠度的估计并讨论了其性质.     

Response surface methodology: A neural network approach

Response surface methodology is used to optimize the parameters of a process when the function that describes it is unknown. The procedure involves fitting a function to the given data and then using optimization techniques to obtain the optimal parameters. This procedure is usually difficult due to the fact that obtaining the right model may not be possible or at best very time consuming.In this paper, a two-stage procedure for obtaining the best parameters for a process with an unknown model is developed. The procedure is based on implementing response surface methodology via neural networks. Two neural networks are trained: one for the unknown function and the other for derivatives of this function which are computed using the first neural network. These neural networks are then used iteratively to compute parameters for an equation which is ultimately used for optimizing the function. Results of some simulation studies are also presented.     

应力为GBVE分布强度为指数分布下并联结构可靠度的估计

考虑应力服从GBVE分布,强度服从指数分布的应力—强度模型,分别在应力参数未知和强度参数未知情形下给出了该模型在并联系统下可靠度的估计并讨论了其性质.     

Adaptive modified function projective synchronization of unknown chaotic systems with different order

This paper investigates the modified function projective synchronization (MFPS) between two different dimensional chaotic systems with fully unknown or partially unknown parameters via increased order. Based on the Lyapunov stability theorem and adaptive control method, a unified adaptive controller and parameters update law can be designed for achieving the MFPS of the two different chaotic systems with different orders. Numerical simulations are presented to show the effectiveness of the proposed synchronization scheme.