关于完全非线性函数的非线性度的界

非线性函数在编码和密码领域中扮演着非常重要的角色,衡量函数的非线性性质很重要。非线性度和差分概率是衡量函数非线性性质的重要指标,差分概率均匀的函数称为具有完全非线性的函数。文中改进了Carlet和Ding所给出的完全非线性函数的非线性度的上界和下界,提出了更好的界的优化问题模型。     

一种新的大信号射频功率器件建模方法

对小信号网络分析而言,单一的S参数已足够描述器件的特性.但对大信号网络分析而言,则需要更多的数学工具来描述器件的特性.本文采用了一个新的适用于描述大信号非线性特性的描述函数——非线性散射函数.利用非线性散射函数可以完成对大信号射频功率器件的精确建模.     

A recurrent neural network for nonlinear convex optimization subject to nonlinear inequality constraints

This paper presents a novel recurrent neural network for solving nonlinear convex programming problems subject to nonlinear inequality constraints. Under the condition that the objective function is convex and all constraint functions are strictly convex or that the objective function is strictly convex and the constraint function is convex, the proposed neural network is proved to be stable in the sense of Lyapunov and globally convergent to an exact optimal solution. Compared with the existing neural networks for solving such nonlinear optimization problems, the proposed neural network has two major advantages. One is that it can solve convex programming problems with general convex inequality constraints. Another is that it does not require a Lipschitz condition on the objective function and constraint function. Simulation results are given to illustrate further the global convergence and performance of the proposed neural network for constrained nonlinear optimization.     

Modeling Harmonic Distortions Caused by Nonlinear Op-Amp DC Gain for Switched-Capacitor Sigma–Delta Modulators

Op-amps are crucial components in sigma-delta modulators (SDMs). As device dimensions and supply voltages continue to scale down, it is increasingly critical to determine a suitable op-amp dc gain. If the dc gain is set too high, then the op-amp consumes too much power; if the dc gain is too small, then nonlinear distortion becomes serious. However, there exists no efficient approach for selecting dc gains. In this brief, we propose to use a nonlinear function to model nonlinear op-amp dc gain curves. Then, this nonlinear function is employed to derive an SDM nonlinear distortion model as a function of SDM system parameters. The obtained SDM nonlinear distortion model can subsequently be used to compute the minimum required op-amp dc gain such that nonlinear distortions are kept under a tolerable value. The nonlinear dc gain curve model and the SDM nonlinear distortion model proposed in this brief are verified by behavior simulations and transistor-level simulations.     

一种分析非线性振荡器频率及振幅灵敏度的新方法

本文提出了一种基于Volterra函数分析非线性振荡器频率及振幅灵敏度的新方法,该方法不仅克服了传统分析方法所受到的非线性元件应为弱非线性,非线性振荡幅度应足够小这两方面的限制,而且还可以用来分析高阶非线性振荡电路.本文对该方法进行了理论上的探讨.     

Measured and modeled conducted susceptibility characteristics of alithium niobate electrooptic modulator

The electromagnetic (EM) susceptibility of an electrooptic (E-O) modulator is characterized. A nonlinear susceptibility model and measured results are presented for a Crystal Technology MZ385P optical guided-wave intensity modulator. The transfer function for the E-O modulator is expressed in closed form and a Bessel function expansion of this transfer function is used to predict nonlinear effects. The nonlinear effects which are modeled include gain compression, radiant power offset, harmonic generation, and intermodulation generation. The model predictions are compared to measured data at in-band and out-of-band frequencies. At in-band frequencies, excellent agreement is obtained between measured and modeled nonlinear product levels. At out-of-band frequencies, variations in the nonlinear output product levels are explained by the frequency-dependent gain characteristics of the modulator     

含非线性缺陷的光子晶体异质结构中的光学响应

为了得到非线性介质中的光学响应,考虑了光通过含有非线性缺陷的一维光子晶体异质结构的情况,对缺陷层的介电函数采取δ函数近似的方法,得到了具有非线性缺陷的一维光子晶体异质结构中的光学响应表达式。结果表明,非线性缺陷存在时,在光学响应中会出现双稳态、多稳态等特性。讨论了双稳态及其多稳态的形成条件,并与考虑缺陷层厚度时的结论进行了比较,为构造零阈值的激光器和非线性光学器件的初步设计提供了有益的理论参考。     

Adaptive algorithms with nonlinear data and error functions

The tools of nonlinear system theory are used to examine several common nonlinear variants of the LMS algorithm and derive a persistence of excitation criterion for local exponential stability. The condition is tight when the inputs are periodic, and a generic counterexample is demonstrated which gives (local) instability for a large class of such nonlinear versions of LMS, specifically, those which utilize a nonlinear data function. The presence of a nonlinear error function is found to be relatively benign in that it does not affect the stability of the error system. Rather, it defines the cost function the algorithm tends to minimize. Specific examples include the dead zone modification, the cubed data nonlinearity, the cubed error nonlinearity, the signed regressor algorithm, and a single-layer version of the backpropagation algorithm     

Liapunov function of a sixth-order nonlinear system

A formulation of a Liapunov function is given for the stability study of a sixth-order system characterized by a nonlinear function φ(x). Fifth-order and fourth-order systems with a nonlinear function φ(x) are given as special cases.     

一种非线性动态网络的离散分析算法设计及实现

在非线性动态网络响应分析中,采用Volterra级数法可以导出与线性系统传递函数相似的非线性传递函数,能使非线性系统用线性化和系统化方法达到精确分析.本文利用方波函数的积分变换具有将时域内的微分、积分运算变换成方波域内的矩阵代数运算的性质,将一类非线性动态网络响应求解的Volterra级数解的连续时域递推算法转化为离散算式,解决了连续算式中广义卷积积分的迭加计算麻烦的问题.文中给出了该算法,仿真结果证明了它的有效性.     

基于微分搜索的高光谱图像非线性解混算法

针对线性混合模型在实际高光谱图像解混过程中的局限性,提出一种新的基于微分搜索的非线性高光谱图像解混算法.在广义双线性模型的基础上采用重构误差作为解混的目标函数,将非线性解混问题转化为最优化问题.将目标函数中的待求参数映射为微分搜索过程中的位置变量,利用微分搜索算法对目标函数进行优化求解.在求解过程中,通过执行搜索范围控制等机制满足高光谱图像解混的约束要求,进而求得丰度系数和非线性参数,实现非线性高光谱图像解混.仿真数据和真实遥感数据实验结果表明,所提出的非线性解混算法可以有效克服线性模型下解混算法的局限性,避免了由于使用梯度类优化方法而易陷入局部收敛的问题,较之其它高光谱图像解混算法具有更好的解混精度.     

Piecewise Nonlinear Approach to the Implementation of Nonlinear Current Transfer Functions

A piecewise nonlinear approach to the nonlinear circuit design has been proposed in this paper. It is to approximate a target nonlinear transfer function by a particular combination of selected nonlinear pieces. The pieces can be produced by one or more analog blocks involving nonlinear devices. This approach can be applied to design nonlinear circuits to implement various current transfer functions. By controlling the operation modes of the transistor pair in a simple current mirror, one can modulate the current transfer function in a radical or fine-tuning manner. It is thus possible for the same current mirror to generate very different nonlinear pieces in different sections of its input range. In order that the control is done automatically by the input current, or in other words, the operation of the transistors is made to be input-current-dependent in a controlled manner, a series structure of two transistors has been proposed to be incorporated in the current mirror. The dependency can be made different by placing the structure in different places of the current mirror and/or by making the two transistors complementary or not, which makes the variations of the nonlinear function. Several current mirrors have been designed. Each of them consists of a very small number of transistors and performs a defined nonlinear current transfer function. The circuits have been simulated with HSPICE to validate the functions. The successful results have been obtained and are presented in the paper.     

Determination of optimum nonlinear systems for generalized error criteria based on the use of gate functions

A generalization of the error criteria in the analysis of optimum nonlinear systems is presented. The experimental and analytical techniques presented are based upon the expansion of the nonlinear system in the orthogonal set of gate functions that were introduced into the study of nonlinear systems by Bose in 1955. It is shown that, for various error criteria, the coefficients in the expansion can be determined independently of each other. By making use of this result, methods are developed for the determination of nonlinear systems with and without memory, for which an arbitrary weighted function of the error or the probability of an arbitrary function of the error is a minimum.     

S型非线性调频信号及其多普勒频率范围

给出了S型非线性调频信号的传递函数，由传递函数算出了群延迟、频谱函数和模糊函数表达式，并根据模糊函数获得了S型调频信号的各项基本性能。     

A note on solving a system reliability problem involving nonlinear constraints

This paper is concerned with maximizing a system reliability function subject to nonlinear constraints. Numerical examples from the literature are handled by a general nonlinear programming algorithm, which can deal with the positive-integer variables of this reliability problem without special difficulties. The computational results presented in this paper suggest that the computer program listed here can be useful as a model for maximizing the system reliability function subject to the nonlinear constraints used here. In addition, because of the general applicability of the nonlinear programming algorithm, other system reliability functions and nonlinear constraints different from the ones used in this paper can also be accommodated.     

Control of Chua's circuit with a cubic nonlinearity via nonlinear linearization technique

This paper addresses the controlling chaos problem of a cubic variant for the original Chua's circuit. A conventional input-output transfer function of a linearized system and a nonlinear linearization technique for a nonlinear system are also presented. According to analytical results, at equilibrium, the notion of local phase-minimality of the nonlinear system is equivalent to that of the linear system's transfer function. Our results also demonstrate that the controlled Chua's circuit, while considering a certain state as the system output, is an input-output linearizable minimum-phase system. In addition, nonlinear control laws are derived such that each state asymptotically tracks its corresponding desired trajectory while maintaining the boundedness of all signals inside the system.     

Fourier Analysis of Nonlinear Fluid Systems

Some results are given concerning the apparent transfer function measured by the cross-spectrum method on some special nonlinear systems. The nonlinear behavior in question is not evidenced by the usual coherence function. A method which characterizes both the linear and the nonlinear parts of the input-output relationship is then proposed.     

Kernel RX-algorithm: a nonlinear anomaly detector for hyperspectral imagery

We present a nonlinear version of the well-known anomaly detection method referred to as the RX-algorithm. Extending this algorithm to a feature space associated with the original input space via a certain nonlinear mapping function can provide a nonlinear version of the RX-algorithm. This nonlinear RX-algorithm, referred to as the kernel RX-algorithm, is basically intractable mainly due to the high dimensionality of the feature space produced by the nonlinear mapping function. However, in this paper it is shown that the kernel RX-algorithm can easily be implemented by kernelizing the RX-algorithm in the feature space in terms of kernels that implicitly compute dot products in the feature space. Improved performance of the kernel RX-algorithm over the conventional RX-algorithm is shown by testing several hyperspectral imagery for military target and mine detection.     

二进神经网络非线性移位寄存器的综合

本文利用二进神经网络及其学习算法特点和对布尔函数的映射能力,设计了一个精巧的非线性移位寄存器的综合算法,同时得到序列非线性复杂度的移位寄存器的反馈布尔函数.此综合算法简单可靠,所需存储运算量小.     

非线性离散时间系统的自适应函数观测器

针对一大类非线性离散时间系统提出了一种自适应函数观测器(AFO)。通过引入状态变换，得到了一类降阶形式的状态估计问题。采用一种稍加修改的强跟踪滤波算法估计降阶状态向量，然后利用降阶状态向量估计非线性状态函数。给出了AFO局部渐近收敛的充分条件。数值仿真示例显示AFO是一种具有强跟踪性质的自适应观测器，能在估计非线性状态函数的同时准确估计未知时变参数。