关于一类Lagrange函数族的存在条件

研究力学系统的Lagrange函数族,根据从第一积分直接构造Lagrange函数的方法,提出一类Lagrange函数族的结构,导出这类Lagrange函数族的存在条件和直接构造方法.举例说明所得结果的应用.     

从第一积分构造Lagrange函数的直接方法

提出力学系统Lagrange函数和第一积分之间存在一种新关联,在此基础上给出变分法逆问题的一种新的直接解法.证明系统Lagrange函数可以由带修正因子的第一积分构成,导出修正因子应满足的偏微分方程,运用此解法构建不同系统的Lagrange函数和函数族,并讨论新解法的特点.     

利用变量变换构造耗散系统Lagrange函数

提出变系数耗散系统变分法逆问题的一种间接解法.首先利用坐标和时间变量变换将系统运动微分方程化为自伴随方程,计算得到Lagrange函数后,再变换为原来变量以得到给定方程的Lagrange函数.给出两个例子以说明所得结果的应用.     

Lagrange函数族及其存在条件的再研究

再研究由第一积分组成Lagrange函数族的结构及其存在条件,指出同一个函数族有多种表示方式,并给出新形式的函数族的存在条件.     

从运动方程构造Lagrange函数的直接方法

根据对Lagrange函数的结构分析,提出直接从运动微分方程构造一维系统Lagrange函数新的一般方法和6种特殊方法.利用提出的方法导出若干运动微分方程的Lagrange函数.直接构造法证实一个系统具有多个不同而等效的Lagrange函数,甚至是Lagrange函数族.这种直接构造法也是构造Lagrange对称性并导出对应守恒量的一种途径.     

结合增广Lagrange罚函数的约束优化差分进化算法

利用增广Lagrange罚函数处理问题的约束条件,提出了一种新的约束优化差分进化算法。基于增广Lagrange惩罚函数,将原约束优化问题转换为界约束优化问题。在进化过程中,根据个体的适应度值将种群分为精英种群和普通种群,分别采用不同的变异策略,以平衡算法的全局和局部搜索能力。用10个经典Benchmark问题进行了测试,实验结果表明,该算法能有效地处理不同的约束优化问题。     

关于变积的研究

研究变分法逆问题中变积概念及其计算方法.由变积直接构造的是与加速度相关的Lagrange函数,再通过规范变换可以得到位形空间中的Lagrange函数.这表明这种构造Lagrange函数的方法与Engels方法一致.     

由符号函数与绝对值函数派生的非线性函数

人工智能控制中逻辑判断必不可少。因为可以采用简单的非线性函数进行逻辑判断,所以在实际应用中,可以用适当构造的非线性函数来实现部分的智能控制。因此,提出了一种采用符号函数和绝对值函数构造特殊非线性函数的方法,并讨论了利用这些特殊的非线性函数逼近任意的第一类非连续函数的问题。     

Lagrange优化前馈神经网络盲多用户检测算法

提出了一种前馈神经网络盲多用户检测算法.该算法利用恒模准则构造了一个代价函数,给出了该算法的约束条件.利用增广Lagrange函数方法对带约束的代价函数进行优化求解,获得前馈神经网络网络权值和参数的迭代公式,从而实现了盲多用户检测.利用计算机对增广Lagrange函数优化的前馈神经网络盲多用户检测算法进行仿真.仿真结果表明,新算法具有较好的误码率及收敛特性等性能.     

对称布尔函数的算术相关函数

算术相关函数是最近提出的一种研究布尔函数密码学性质的方法,该方法通过定义多元2-adic数上的加法和乘法运算,构建一种新的环结构,实现对经典相关函数的带进位计算的模拟。首先介绍了算术相关函数的定义,并针对具有良好密码学性质的对称布尔函数讨论了其算术相关函数的性质和取值,最后利用对称布尔函数的实值对称性证明了对称布尔函数的算术自相关函数也是一个与向量的重量有关的实值对称函数,至多是n+1值的。     

RLC器件数字测量仪设计与实现

为了精确测量分立元件的参数,提出以单片机为控制核心的RLC器件测量仪的设计制作方法。该测量仪以STC12C5A60S2单片机为控制核心,以DDSAD9850自制信号源和RLC测试电路为主要模块设计实现了对电阻、电感和电容元器件进行测量的仪器,使用16位的模数转换芯片AD7705对L、R、C分压有效值进行实时采样,自制信号源频率可达0.5HZ-10MHZ。经实验验证,本文设计的RLC器件测量仪电阻测量最大误差≤1%,电容测量最大误差≤1%,电感测量最大误差≤1.5%。     

应用谐振法实现高性能RLC测量

谐振法是测量RLC参数的三大方法之一,要解决的主要问题是频率稳定性及测试时间较长的问题,以DDS作为激励信号,能较好地满足谐振法高精度测量的要求。文中硬件给出了具体电路参数,软件给出了相应软件流程,总结了提高性能的方法。     

Study of compact microstrip lowpass filter with improved performance using defected ground structure

A compact lowpass filter (LPF) with wide stopband which uses four non‐uniform cascaded defected ground structure (DGS) units along with a 50 Ω microstrip line is reported in this article. Each DGS unit, which consists of a combination of three isosceles U‐shaped DGSs is analyzed in terms of an equivalent RLC circuit model. Every DGS of the DGS unit along with microstrip line provides one attenuation pole. It is found through performance comparison of the proposed U‐shaped DGS with dumbbell‐ and fork‐shaped DGSs that the proposed U‐shaped DGS is compact and provides higher quality factor. Further, the modeling of the proposed LPF is carried out using equivalent RLC circuit model. The results obtained through numerical and circuit simulations are compared. The proposed LPF has size of 14.44 mm × 3.4 mm, 3‐dB cut‐off frequency of 14.2 GHz, and greater than 40 dB and 22 dB stopband rejection up to 21.8 GHz and 30 GHz respectively. The proposed LPF is fabricated and experimentally tested. The experimental results are nearly in agreement with corresponding numerical/circuit simulation results.     

特定条件的二阶系统的最优控制解析解

针对给控制对象或控制过程加以外部和内部控制作用,使控制对象或控制过程按照某种最优化方法进行,这种最优方式用一个人为确定的目标函数或性能指标为最优来表示。求解了在指定端点固定条件以及目标函数情况下二阶系统的最优控制解析解。以二阶RLC串联充电电路为例,讨论了在指定时间内对电容充电到指定电压,同时在充电过程中保证充电电压最小,发热量最小的最优控制,对控制系统设计有一定指导意义。     

灰参数电路的控制问题及系统状态仿真分析

实际系统模型难以使用确定参数进行描述,含有灰参数的电路普遍存在.基于灰数、灰色控制和电路分析等方法,对灰色电路系统进行分析,具有一定的理论和实践意义.以某一灰色RLC电路模型为例,研究其能控、能观、稳定性、电路仿真等问题.灰色电路的研究有助于灰色系统模型的仿真验证和硬件实现,丰富灰色电路和灰色控制等领域,也可应用于不确定性电路分析、系统建模和控制等问题.     

基于USB接口程控仪器的虚拟测试平台

介绍一种利用USB接口组成的程控仪器虚拟测试平台,给出了平台的基本构成和在LabVIEW环境下测试软件的设计思想,并以RLC串联谐振电路特性测试为例,介绍了该平台的开发和应用方法。     

Time-domain analysis methodology for large-scale RLC circuits and its applications

With soaring work frequency and decreasing feature sizes, VLSI circuits with RLC parasitic components are more like analog circuits and should be carefully analyzed in physical design. However, the number of extracted RLC components is typically too large to be analyzed efficiently by using present analog circuit simulators like SPICE. In order to speedup the simulations without error penalty, this paper proposes a novel methodology to compress the time-descritized circuits resulted from numerical integration approximation at every time step. The main contribution of the methodology is the efficient structure-level compression of DC circuits containing many current sources, which is an important complement to present circuit analysis theory. The methodology consists of the following parts: 1) An approach is proposed to delete all intermediate nodes of RL branches. 2) An efficient approach is proposed to compress and back-solve parallel and serial branches so that it is error-free and of linear complexity to analyze circuits of tree topology. 3) The Y toπtransformation method is used to error-free reduce and back-solve the intermediate nodes of ladder circuits with the linear complexity. Thus, the whole simulation method is very accurate and of linear complexity to analyze circuits of chain topology. Based on the methodology, we propose several novel algorithms for efficiently solving RLC-model transient power/ground (P/G) networks. Among them, EQU-ADI algorithm of linear-complexity is proposed to solve RLC P/G networks with mesh-tree or mesh-chain topologies. Experimental results show that the proposed method is at least two orders of magnitude faster than SPICE while it can scale linearly in both time- and memory-complexity to solve very large P/G networks.     

Power balancing for a new class of non-linear systems and stabilization of RLC circuits

In this paper the method of power shaping, as recently introduced for the stabilization of non-linear RLC circuits, is generalized to a larger class of systems showing similarities (and important differences) with the class of port-controlled Hamiltonian systems. Other than for port-controlled Hamiltonian systems, the stabilization of these new systems is not stymied by a ‘dissipation obstacle’ and, in fact, every power-shaping controller is power balancing as well. It is shown that the power-shaping controller can be realized as a port-controlled Hamiltonian system connected by means of a gyrator to the plant. The theoretical results are applied to the class of non-linear RLC circuits described by Brayton–Moser's equations, and a physical implementation of the controllers in terms of standard electrical circuit elements is given.     

一种新型瞬变电磁发射机去过冲系统设计

针对瞬变电磁发射机发射电流过冲造成探测盲区的问题,提出了一种新型瞬变电磁发射机去过冲系统设计方案。该方案在发射线圈两端并联一个优化的RLC二阶电路,在发射电流下降到接近零时接通该电路,让发射电流按指数衰减,从而有效去除电流过冲。仿真与实验结果表明,该方案能够去除发射电流的过冲振荡,减小探测盲区。     

Continuity of latent variable models

The authors study the continuity of the behavior of dynamical systems as a function of the parameters in their behavioral equations. A system is defined in terms of its behavior and continuity requires that this behavior be continuous in the limit. The problem is demonstrated by means of an example involving an RLC circuit whose port behavior exhibits a surprising discontinuity as a function of the numerical values of the elements in the circuit. The main result states that a system described by means of difference equations involving manifest (external) and latent (internal) variables will have a continuous behavior in the limit if the limit system is observable