Decomposition‐based multiinnovation gradient identification algorithms for a special bilinear system based on its input‐output representation

This article considers the parameter estimation for a special bilinear system with colored noise. Its input‐output representation is derived by eliminating the state variables in the bilinear system. Based on the input‐output representation of the bilinear system, a multiinnovation generalized extended stochastic gradient (MI‐GESG) algorithm is proposed by using the multiinnovation identification theory. Furthermore, a decomposition‐based multiinnovation (ie, hierarchical multiinnovation) generalized extended stochastic gradient identification (H‐MI‐GESG) algorithm is derived to enhance the parameter estimation accuracy by using the hierarchical identification principle, and a GESG algorithm is presented for comparison. Compared with the existing identification algorithms for the bilinear system, the proposed MI‐GESG and H‐MI‐GESG algorithms can generate more accurate parameter estimation. Finally, a simulation example is provided to verify the effectiveness of the proposed algorithms.     

Extended stochastic gradient identification algorithms for Hammerstein–Wiener ARMAX systems

An extended stochastic gradient algorithm is developed to estimate the parameters of Hammerstein–Wiener ARMAX models. The basic idea is to replace the unmeasurable noise terms in the information vector of the pseudo-linear regression identification model with the corresponding noise estimates which are computed by the obtained parameter estimates. The obtained parameter estimates of the identification model include the product terms of the parameters of the original systems. Two methods of separating the parameter estimates of the original parameters from the product terms are discussed: the average method and the singular value decomposition method. To improve the identification accuracy, an extended stochastic gradient algorithm with a forgetting factor is presented. The simulation results indicate that the parameter estimation errors become small by introducing the forgetting factor.     

不同阶分数阶混沌系统的同步与参数辨识

针对不确定分数阶混沌系统的同步和参数辨识问题,提出一种新的方法,即用不同阶分数阶系统来同步和参数辨识.利用主动控制和预控制量方法,基于分数阶混沌系统稳定性理论和自适应控制理论,设计控制器,实现不同阶分数阶混沌系统之间的同步和参数辨识.理论和仿真结果实现了不同阶Chen 系统间的同步和辨识,表明了该方法的有效性.     

分数阶随机Duffing系统的Hopf分岔

运用正交多项式逼近原理，研究了分数阶随机Duffing系统在零平衡点的Hopf分岔．首先，运用Laguerre正交多项式逼近法将含有随机参数的分数阶Duffing系统转化为等价的确定性系统，然后通过数值计算求得其响应．最后，利用两个引理求得等价系统发生Hopf分岔行为的临界值，并通过数值模拟验证了理论分析结果．     

Recursive identification of time-varying systems: Self-tuning and matrix RLS algorithms

In this paper, a new parallel adaptive self-tuning recursive least squares (RLS) algorithm for time-varying system identification is first developed. Regularization of the estimation covariance matrix is included to mitigate the effect of non-persisting excitation. The desirable forgetting factor can be self-tuning estimated in both non-regularization and regularization cases. We then propose a new matrix forgetting factor RLS algorithm as an extension of the conventional RLS algorithm and derive the optimal matrix forgetting factor under some reasonable assumptions. Simulations are given which demonstrate that the performance of the proposed self-tuning and matrix RLS algorithms compare favorably with two improved RLS algorithms recently proposed in the literature.     

基于分数阶积分器的分数阶混沌系统状态观测器同步研究

提出了一种基于分数阶积分器的分数阶混沌系统状态观测器同步算法。通过引入一个新的变量,该变量是将驱动系统的输出信号与传输信道中干扰的和进行分数阶积分处理,然后再作为输入信号加到观测系统中,以便实现分数阶混沌系统的状态观测系统同步。然后利用Lyapunov稳定性理论和线性矩阵不等式证明了该方法的正确性。将该同步方法应用于分数阶Chen混沌系统,得出了同步误差曲线,仿真结果表明了该同步方法的有效性,最终实现了分数阶混沌系统的状态观测器同步。     

基于自适应密度估计的系统参数辨识

针对噪声分布未知的ARMAX系统,提出了一种自适应非参数噪声密度估计方法,由估计误差动态调整高斯核函数的全局带宽和局部带宽,实现了未知噪声分布密度的自适应估计;通过极小化似然函数,给出了基于噪声密度估计的参数辨识迭代算法,分析了算法的收敛性并给出了算法收敛的充分条件.仿真结果表明本文提出的算法在系统噪声未知时具有较强的抗噪能力和良好的收敛性.     

反馈非线性系统随机梯度辨识算法及其收敛性

反馈非线性受控自回归系统是由前向通道的受控自回归模型和反馈通道的静态非线性构成, 这类系统经过参数化后得到双线性参数辨识模型. 本文通过对辨识模型中双线性参数乘积项进行分解, 基于梯度搜索原理, 提 出了反馈非线性系统的随机梯度辨识算法. 为了改善随机梯度算法的收敛速度, 引入遗忘因子, 文章给出了遗忘因子随机梯度算法, 利用随机过程理论, 建立了随机梯度算法的参数估计收敛定理, 证明了算法的收敛性. 最后, 通过数值仿真验证了算法的有效性.     

变遗忘因子多新息随机梯度算法双馈电机参数辨识

针对电机运行过程中参数变化特点,基于多新息辨识理论与随机梯度辨识算法理论,结合变遗忘因子,提出了基于变遗忘因子多新息随机梯度算法的双馈电机参数辨识方法。该方法考虑到双馈电机非线性强耦合,采用定子磁链定向的矢量控制技术,搭建双馈电机矢量控制系统采集数据,并推导dq坐标系下电机参数辨识模型的标准形式,根据算法辨识出电机电感及电阻参数。仿真结果验证了该算法的有效性。     

分数阶混沌系统的Simulink动态仿真及硬件设计

由于目前分数阶混沌的理论分析和硬件设计都比较烦琐,提出了分数阶混沌系统的Simulink动态仿真方法。以分数阶Jerk系统为例,根据分数阶系统方程搭建分数阶混沌系统仿真模型,可动态地观察系统变量的变化规律。仿真结果表明,分数阶混沌系统的Simulink动态仿真方法是一种切实可行的分析方法。此外,还给出了分数阶混沌系统直接进行硬件设计的方法,这为分数阶混沌系统的数字设计提供了新的思路。     

Convergence of fixed‐point iteration for the identification of Hammerstein and Wiener systems

Convergence property of the iterative algorithm for Hammerstein or Wiener systems is generally hard to establish because of the existence the unmeasurable internal variables in such systems. In this paper, a fixed‐point iteration is introduced to identifying both Hammerstein and Wiener systems with a unified algorithm. This newly proposed estimation algorithm gives consistent estimates under arbitrary nonzero initial conditions. In addition, the errors of the estimates are established as functions of the noise variance, and thus how the noise affects the quality of parameter estimates for a finite number of data points is made clear. Copyright © 2012 John Wiley & Sons, Ltd.     

基于分数阶陈氏混沌系统的图像加密算法

由于分数阶混沌动力学系统比整数阶系统具有更复杂的动力学特性,且能为图像加密方案提供更多的自由度,基于分数阶陈氏混沌系统,提出了一种图像加密方法。在发送端,驱动系统产生混沌信号,利用混沌信号扰乱明文图像的像素位置,将扰乱后的图像掩盖在混沌信号中,得到传输的密文图像。在接收端,通过同步系统去掩盖,进行像素位置扰乱的逆操作,恢复明文图像。最后对提出的加密算法进行了安全性分析。实验结果表明,该加密算法安全性高,具有良好的研究价值和应用前景     

On identification of Hammerstein and Wiener model with application to virtualised software system

This paper proposes a system identification method for estimating virtualised software system dynamics within the framework of a Hammerstein–Wiener model. Building on the authors’ previous work in identification and control of the software systems, the approach utilises frequency sampling filter structure to describe the linear dynamics and B-spline curve functions for the inverse static output nonlinearity. Furthermore, the issue on parameter selection for B-spline model approximation of scatter data is addressed by using a data clustering method. An experimental test-bed of virtualised software system is established to generate real observational data which are used to confirm the performance of the proposed approach. The identification results have shown that the model efficacy is increased with the proposed approach because the dimension of the nonlinear model can be significantly reduced while maintaining the desired accuracy.     

有理模型辨识的两类新方法——混合迭代与柔性最小二乘法

针对有理模型提出两类辨识方法.首先提出基于递阶辨识思想的混合辨识方法,将模型分解为分子和分母两个子模型,分别用最小二乘法辨识分子参数,用粒子群算法和智能多步长梯度迭代算法辨识分母参数.由于降低了模型维数,且信息向量与噪声不相关,相对于传统的偏差补偿最小二乘算法,混合迭代法可以提高辨识精度并降低计算量.然后,为消除模型结构已知的假设,且充分利用最新数据更新系统参数,提出柔性递推最小二乘辨识方法,将有理模型转化为时变参数系统,进而辨识出时变系统的参数.仿真例子验证了所提出方法的有效性.     

非线性系统Wiener模型辨识

本文采用不同幅值的三电平伪随机m序列作为输入信号,辨识了离散非线性系统Wiener模型的线性脉冲响应函数和非线性增益系数.同时讨论了参数估计的统计特性及其区间估计,并附有仿真结果.     

基于PSO算法的微生物间歇发酵动力学参数辨识

主要根据微生物间歇培养过程的特征、动态行为及实验数据,建立了能够更好反映间歇发酵过程的简化的多阶段参数辨识模型,然后证明了该模型中最优参数的存在性;最后结合模型特点构造了一种改进的粒子群优化（PSO）算法求得最优参数,并利用所得的参数进行过程仿真。结果表明该模型和算法大大减少了实验数据和计算数值之间的误差,能够更好地模拟微生物间歇发酵过程。     

广义离散随机线性系统降阶Wiener滤波、平滑和预报器

应用现代时间序列方法 ,基于自回归滑动平均 (ARMA)新息模型、白噪声估值器和观测预报器 ,对于广义离散随机线性系统 ,提出了降阶Wiener状态估值器 ,可统一处理滤波、平滑和预报问题 ,并且能减少计算负担 .仿真例子说明了算法的有效性     

Parameter estimation and system identification for continuously-observed quantum systems

This paper gives an overview of parameter estimation and system identification for quantum input–output systems by continuous observation of the output field. We present recent results on the quantum Fisher information of the output with respect to unknown dynamical parameters. We discuss the structure of continuous-time measurements as solutions of the quantum Zakai equation, and their relationship to parameter estimation methods. Proceeding beyond parameter estimation, the paper also gives an overview of the emerging topic of quantum system identification for black-box modelling of quantum systems by continuous observation of a travelling wave probe, for the case of ergodic quantum input–output systems and linear quantum systems. Empirical methods for such black-box modelling are also discussed.