MIMO非线性系统的多模型建模方法

针对实际工业过程中多变量系统存在着非线性、工况范围广的特点,本文提出了一种新的多模型建模方法.首先对系统调度变量进行满意模糊c均值聚类,在此基础上采用基于加权性能指标的多模型辨识算法辨识多模型系统,得到的模型在全局拟合与局部特性之间取得良好的权衡,同时能得到每个局部模型的适用域.以典型pH中和过程为对象,采用上述建模方法建立其系统多模型,仿真结果验证了该建模方法的有效性.     

Volterra Systems with Random Inputs: A Formalized Approach

The object of this work is to investigate the problem of Volterra systems driven by random inputs. General expressions for the second-order output statistics of a Volterra system are obtained and formalized. The input-output crosscorrelation and output autocorrelation functions are expressed in terms of higher order input autocorrelation functions. In the frequency domain, the cross-power and output power spectral densities are expressed in terms of higher order input power spectral densities. These expressions are used to obtain closed-form equations for the cross-power and output power spectral densities of a Volterra system driven by a real, stationary, zero-mean Gaussian input.     

MIMO非线性系统辨识：Volterra级数法

本文讨论了一般ＭＩＭＯ非线性系统的Ｖｏｌｔｅｒｒａ级数表示,给出并证明了Ｖｏｌｔｅｒｒａ核矩阵存在的条件。提出了两种辨识Ｖｏｌｔｅｒｒａ核矩阵的方法,即随机响应法与脉冲响应法。给出了利用系统的输入输出信号计算Ｖｏｌｔｅｒｒａ核矩阵的公式。最后,利用仿真实例验证上述方法的有效性。     

Addendum to "Volterra Systems with Random Inputs: A Formalized Approach"

A newly derived expression for the higher order crosscorrelation function of two jointly stationary Gaussian random processes is used to determine the output autocorrelation function of a Volterra system driven by a Gaussian input and to simplify a previously published expression for the output power spectral density and its derivation.     

非线性参量激励系统的一种分析方法

本文提出一种分析非线性参量激励系统的新方法，这一方法基于等效小参量法原理，容易求得基波修正量和高次谐波的表达式，原理和实例表明，新方法适和于高阶非线性参量激励系统，所得结果解析性强，具有符号分析的优点。     

A New Approach to Variable Selection Using the TLS Approach

The problem of variable selection is one of the most important model selection problems in statistical applications. It is also known as the subset selection problem and arises when one wants to explain the observations or data adequately by a subset of possible explanatory variables. The objective is to identify factors of importance and to include only variables that contribute significantly to the reduction of the prediction error. Numerous selection procedures have been proposed in the classical multiple linear regression model. We extend one of the most popular methods developed in this context, the backward selection procedure, to a more general class of models. In the basic linear regression model, errors are present on the observations only, if errors are present on the regressors as well, one gets the errors-in-variables model which for Gaussian noise becomes the total-least-squares (TLS) model, this is the context considered here     

一种新的非线性Volterra优化算法

文章提出了非线性信号处理中绝对贡献因子的概念,并在此基础上提出了基于绝对贡献因子的自适应Volterra优化算法,该算法能够较好的区分非线性扩展向量中的冗余项和最优项,优化后的算法能够使其计算量减小30%左右。     

弱非线性动态系统Volterra核自动测试系统的研究

本文讨论弱非线性动态系统Ｖｏｌｔｅｒｒａ核自动测试系统的研制，应用Ｖｏｌｔｅｒｒａ泛函级数和计算机技术于非线性系统，本文结合频率域多点测量弱非线性系统前二阶核的算法ＱＭＭＰ２及测量前三阶核的算法ＱＭＭＰ３，设计了自动测试系统。本文给出应用该系统的两个测量实例。     

基于循环统计量的Volterra系统最大记忆长度估计

本文对记忆长度信息估计问题进行了论述.对于最大记忆长度信息的估计,基于循环自相关,直接使用或串接平方项的判定方法,只对系统为满Volterra系统或部分稀疏系统的情况成立.本文利用Volterra系统输出信号的线性循环自相关、非线性循环自相关以及高阶循环累积量,结合同构、组合同构、子集结构的概念和系统分阶的思想,提出了Volterra系统各阶子系统最大记忆长度信息估计方法,给出了最大记忆长度信息的判决准则,仿真结果表明:文中提出的盲判定方法可以获得更多正确的系统相关信息.     

用于在线辨识非线性系统的可变正交小波网络

对于在线辨识非线性系统,传统的小波网络缺乏有效的算法。本文在正交小波网络的基础上,提出一种利于实时应用的可变正交小波网络,给出了其结构变化和参数调整的策略,并对建模误差的变化进行了分析。最后用于辨识非线性动态系统,仿真结果验证了该方法的可行性和有效性。     

A Control Lyapunov Function Approach to Stabilization of Affine Nonlinear Systems with Bounded Uncertain Parameters

This paper considers the robust stabilization problem of a class of affine nonlinear systems with bounded uncertain time-invariant parameters. A robust control Lyapunov function (RCLF) is introduced for the considered system. Based on the RCLF, a globally asymptotically stabilizing controller is then designed. The proposed controller is robust under the variant of system parameters. As the applications of the proposed scheme, the stabilization of uncertain feedback linearizable systems and the unified chaotic system are investigated, respectively. A numerical example on the unified chaotic system is also provided to illustrate the effectiveness of the presented method.     

Accurate Nonlinear Volterra Series Analysis for Vertical-Cavity Surface-Emitting Lasers

In this letter, an accurate nonlinear Volterra series analysis for vertical-cavity surface-emitting lasers (VCSELs) is presented. Closed-form expressions for the modulation response, harmonic distortions, and second- and third-order intermodulation distortions are derived. Moreover, the suggested nonlinear model avoids the numerical solution of laser rate equations and provides in-depth insight of a distortion analysis of VCSEL.     

Extension of Volterra Analysis to Weakly Nonlinear Electromagnetic Field Problems with Application to Whistler Propagation

In this study, Volterra analysis is extended to weakly nonlinear electromagnetic field problems. Generalized Green's functions and their Fourier transforms are introduced. These are used to express the nth order system response explicitly in terms of the system input, Although the theory is developed in general, homogeneous media are assumed in the examples for simplicity. Application of the Volterra approach is illustrated by investigating whistler-mode propagation in a cold collisionless electron plasma. After defining the nonlinear differential equations for propagation at an angle theta to the uniform magnetic field, exponential probing inputs are used to generate the generalized Green's functions. The second-order responses, which are expressed in terms of the generalized Green's functions, are examined in detail. Computer programs are used to numerically evaluate the second-order response to a sinusoidally varying time function.     

A New Approach to Realize Variable Gain Amplifiers

A new methodology to develop variable gain amplifiers is developed. The methodology is based on a feedback loop to generate the exponential characteristic, which is required for VGA circuits. The proposed idea is very suitable for applications that require very low power consumption, and as an application, a new current mode variable gain amplifier will be shown. The gain is adapted via a current signal ranges from –7.5 A to +6.5 A. Pspice simulations based on Mietec 0.5 m CMOS technology show that the gain can be varied over a range of 29.5 dB, with bandwidth of 3 MHz at maximum gain value. The circuit operates between ±1.5 V and consumes an average amount of power less than 495 W.     

一类非均匀采样非线性系统的无模型自适应控制

对一类未知的非均匀采样离散时间非线性非仿射系统,基于在受控系统当前工作点处的等价数据模型,利用输入输出数据对伪雅可比矩阵（PJM）的在线估计,设计出相应的无模型自适应控制器.所提出的控制方法具有如下特点：控制器的设计仅需要非均匀采样的输入输出数据,不包含系统模型的任何信息;控制算法计算量小,算法容易实现.最后,通过一个非均匀采样离散时间非线性系统仿真结果验证提出方法的有效性.     

Nonlinear Transient and Distortion Analysis via Frequency Domain Volterra Series

This paper presents a novel approach for transient and distortion analyses for time-invariant and periodically time-varying mildly nonlinear analog circuits. Our method is based on a frequency domain Volterra series representation of nonlinear circuits. It computes the nonlinear responses using a nonlinear current method that recursively solves a series of linear Volterra circuits to obtain linear and higher-order responses of a nonlinear circuit. Unlike existing approaches, where Volterra circuits are solved mainly in the time domain, the new method solves the linear Volterra circuits directly in the frequency domain via an efficient graph-based technique, which can derive transfer functions for any large linear network efficiently. As a result, both frequency domain characteristics, like harmonic and intermodulation distortion, and time domain waveforms can be computed efficiently. The new algorithm takes advantage of identical Volterra circuits for second- and higher-order responses, which results in significant savings in driving the transfer functions. Experimental results for two circuits—a low-noise amplifier and a switching mixer—are obtained and compared with SPICE3 to validate the effectiveness of this method.     

On the Walsh Analysis of Nonlinear Systems

This paper considers some aspects of the analysis of nonlinear systems via Walsh functions. Two basic approaches are investigated. These are 1) a characteristic-function method which assumes a Walsh-transformable nonlinearity and 2) a matrix method that is suitable when the input can be represented by a truncated Walsh series expansion. Illustrative examples are included.