Optimization of configurations of field problem grids using network models

Optimization of grid configurations decreases the discretization error in the numerical solution of field problems. In this paper, the theoretical and algorithmic aspects of optimizing configurations of grids used in equilibrium, potential-type field problems is presented. The criterion for establishing the optimum grid and the steps required to move to the optimum grid are given. Sensitivity network modelling is invoked to systematically form matrices required in the algorithm. One-dimensional examples are presented to illustrate the validity of the approach.     

0-1编码谱系数与最小项展开系数相互转换的代数方法

论文给出了关于0-1编码谱系数与最小项展开系数之间关系的两个定理,在此基础上提出了0-1编码谱系数与最小项展开系数之间转换的代数方法.实例展示了用代数方法实现相互转换的过程.与传统的图形转换方法相比,该方法具有不受变量数限制的优点.     

Solving future equation systems using integral-type error function and using twice ZNN formula with disturbances suppressed

In this paper, for solving future equation systems, two novel discrete-time advanced zeroing neural network models are proposed, analyzed and investigated. First of all, by using integral-type error function and twice zeroing neural network (or termed, Zhang neural network) formula, as the preliminaries and bases of future problems solving, two continuous-time advanced zeroing neural network models are presented for solving continuous time-variant equation systems. Secondly, a one-step-ahead numerical differentiation rule termed 5-instant discretization formula is presented for the first-order derivative approximation with higher computational precision. By exploiting the presented 5-instant discretization formula to discretize the continuous-time advanced zeroing neural network models, two novel discrete-time advanced zeroing neural network models are proposed. Theoretical analyses on the convergence and precision of the discrete-time advanced zeroing neural network models are proposed. In addition, in the presence of disturbance, the proposed discrete-time advanced zeroing neural network models still possess excellent performance. Comparative numerical experimental results further substantiate the efficacy and superiority of the proposed discrete-time advanced zeroing neural network models for solving the future equation systems.     

基于零点的逻辑函数bj图和dj图的转换

图形化简法是逻辑函数化简的有效工具。bi图和西图分别是RM展开式、CRM展开式的图珏表示。通过对RM展开式、CRM展开式系数关系的分析，提出了2种bj图和dj图的图形转换方法，并廷各种方法予以实例说明。对于5变量以下的逻辑函数，这二种方法具有简单、直观等特点。     

最优化计算中的若干新技术

简要介绍了近年来研究十分活跃的以模仿自然与生物优化为特征的几个新的最优化计算方法：根据退火、进化计算和多目标进化优化,并且给出了这些方法的算法描述,最后对单目标和多目标优化问题各给出一个计算实例。     

Recurrent neural dynamics for handling linear equation system with rank-deficient coefficient and disturbance existence

In this paper, for handling discrete-form time-variant linear equation system (DF-TV-LES) with rank-deficient coefficient and disturbance existence, a luminous discrete-time recurrent neural dynamics (DTRND) method is presented. Firstly, the continuous-time recurrent neural dynamics (CTRND) method can be discretized to the DTRND method by using recently-developed 5-instant discretization formula. Secondly, aiming at the situations of rank-deficient coefficient and disturbance existence, corresponding handling methods are presented, respectively. Specifically, on the one hand, under the situation of rank-deficient coefficient, we present an effective method to compute the least-squares solution of DF-TV-LES; on the other hand, under the situation of disturbance existence, integral state of error function is introduced, and then the presented DTRND method possesses a certain performance for restraining different types of disturbances. Finally, comparative numerical experiment substantiates the superiority of the presented DTRND method for handling DF-TV-LES.     

Affine discretization methods for the digital resonant control of uninterruptible power supplies

This paper addresses the discrete-time design and performance evaluation of finite-gain multiple resonant controllers for uninterruptible power supplies – UPS. Two discretization methods that preserve the affinity with respect to time-varying parameters are considered to obtain the discrete-time UPS uncertain model. Based on a state-feedback formulation for the proposed controller, a systematic approach for the robust design of controller gains is derived by the solution of a convex optimization problem subject to linear matrix inequality constraints. Simulation and experimental results in a 3.5 kVA inverter are obtained to compare the effects of distinct sampling frequencies and plant discretization methods with respect to the IEC 62040-3 performance parameters.     

Sparse Bayesian learning approach for discrete signal reconstruction

This study addresses the problem of discrete signal reconstruction from the perspective of sparse Bayesian learning (SBL). Generally, it is intractable to perform the Bayesian inference with the ideal discretization prior under the SBL framework. To overcome this challenge, we introduce a novel discretization enforcing prior to exploit the knowledge of the discrete nature of the signal-of-interest. By integrating the discretization enforcing prior into the SBL framework and applying the variational Bayesian inference (VBI) methodology, we devise an alternating optimization algorithm to jointly characterize the finite-alphabet feature and reconstruct the unknown signal. When the measurement matrix is i.i.d. Gaussian per component, we further embed the generalized approximate message passing (GAMP) into the VBI-based method, so as to directly adopt the ideal prior and significantly reduce the computational burden. Simulation results demonstrate substantial performance improvement of the two proposed methods over existing schemes. Moreover, the GAMP-based variant outperforms the VBI-based method with i.i.d. Gaussian measurement matrices but it fails to work for non i.i.d. Gaussian matrices.     

“连续系统仿真”中数值积分和模型离散化方法的对比教学

数值积分方法和模型离散化方法是连续系统仿真的两种典型方法,其中模型离散化方法相对难以理解,可通过引入对比教学,借助成熟的数值积分方法的知识,让学生对模型离散化方法有深入的理解。文章首先以仿真流程图的模式将模型离散化的快速仿真思想和数值积分法对比,突出其快速的本质;然后通过实例和推导证明了简单替换法和Euler数值积分算法的关系;最后对学生普遍难以理解的模型离散相似法进行深入阐述并和数值积分方法比对讲授,改进了教学效果。     

Adaptive control of printing devices using fractional-order hold circuits adjusted through neural networks

A connectionist method for autotuning the free parameter of a fractional-order hold (FROH) circuit in order to improve the performance of the digitally controlled systems is proposed. Such a technique employs multilayer perceptrons to approximate the mapping between the sampling period/continuous-time parameters of the estimated plant and the optimal value of the FROH adjustable gain. In this way, adaptive discretization systems to improve the stability properties of the resulting discrete-time zeros are implemented. Simulation results are presented in order to illustrate the properties of the complete system applied to two actual digitally controlled printing devices (HP 7090A and low-cost computer printer).     

半导体器件模拟方法研究

主要介绍了半导体器件模拟中的几种物理模型和三角形网格自适应划分的算法。并以泊松方程为例,介绍了如何在网格中进行方程的离散化,以及后期计算方程组的几种数值方法并比较各种算法的优缺点,同时得到解的示意图。     

检测逻辑函数对称性的新方法

本文论述了逻辑函数的Ｒｅｅｄ－Ｍｕｌｌｅｒ展开及ｂ＿ｊ系数图，在此基础上提出了直接检测基于Ｒｅｅｄ－Ｍｕｌｌｅｒ展开的逻辑函数的对称性的新方法。     

H∞ control of singular time-delay systems via discretized Lyapunov functional

This paper addresses the problem of robust H_∞ control for uncertain continuous time singular systems with state delays. A new singular-type complete quadratic Lyapunov-Krasovskii functional (LKF) is introduced, which combines with the discretization LKF method to synthesis problems. An improved bounded real lemma (BRL) is presented to ensure the system to be regular, impulse free and stable with H_∞ performance condition. Based on the BRL, a memoryless state feedback controller is designed via linear matrix inequalities (LMIs), which greatly reduces the disturbance attenuation level. Numerical examples are given to illustrate improvements over some existing results.     

General 9-instant discrete-time Zhang neural network for time-dependent applications

Zhang neural network (ZNN) is widely applied to solving time-dependent problems. For the sake of the implementation on the digital hardware platform, ZNN models need to be discretized. In this paper, as a further study of Zhang et al. discretization (ZeaD) formulas, a novel general 9-instant ZeaD formula is presented, and clear constraints are firstly given with proof. To evaluate the presented 9-instant ZeaD formula, three continuous-time models for time-dependent matrix inversion and pseudoinversion are presented with the help of Getz-Marsden dynamic system (GMDS) and ZNN. Then the corresponding discrete-time models are obtained by using the 9-instant ZeaD formula. According to the comparison experiments, the 9-instant ZeaD formula is substantiated to be effective and consistent with the theory. Furthermore, the problem of mobile angle-of-arrival (AoA) localization is investigated as a more specific and practical problem. In order to overcome the singularity problem of the tangent function in the representation of the AoA localization system, a new representation with sine and cosine functions is presented. Similarly, the continuous-time model is derived and discretized. Through comparison experiments, the discrete-time model obtained by the 9-instant ZeaD formula achieves desirable results, which further show the efficacy of the 9-instant ZeaD formula.     

Interior point penalty functions for constrained minimization

A family of interior point penalty methods for constrained minimization problems are presented and such properties as accuracy and stability of the methods are discussed. A numerical example illustrating the theoretical results is given. Finally some practical guidelines as to which penalty method to apply are presented.     

逻辑函数的减-异或、除-符合展开式的最小化方法

本文根据布尔减-异号、除-符合代数系统中的规范展开式,给出了布尔减-异或、除-符合逻辑函数的代数化简法和图形化简法。     

Riccati differential equations : William T.^Reid. 216 pages,diagrams, 6x9 in. New York,Academic Press Inc. (Mathematics in Science and Industry Series), Vol. 86, 1972. Price, $14.00.

The paper describes methods of carrying out the minimum weight design of finned surfaces of various types. For each type of surface (flat, cylindrical, etc.) two cases are considered. First, a method is described by which it is possible to obtain the optimum surface profile of fins required to dissipate a certain amount of heat from the given surface, there being no restriction on the fin height. This analysis is then extended for the case when the fin height is given. The solutions are presented for a number of cases and the results are discussed to illustrate the importance of various parameters in the design.     

Solution of a linear differential equation of the stretched type via Laguerre functions

A method of using Laguerre functions is presented to obtain approximate solutions of a linear differential equation of the stretched type. The solution is essentially based on the development of two new operational matrices to manipulate, respectively, the differentiation and the stretch via Laguerre functions. It is shown that the proposed method is convenient for computer programming and appears comparable to the accuracy of other methods. Two examples are given for illustration.     

Digital redesign of analog smith predictor for systems with long input time delays

The discretization of the analog Smith predictor by using the prediction-based state-matching digital redesign method for systems with various input time delays was recently investigated in the literature. This paper presents an alternative Chebyshev quadrature state-matching digital redesign method for discretization of the analog Smith predictor for systems with a long input time delay. In order to implement the digitally redesigned Smith predictor by utilizing the output-feedback of the plant, an ideal state reconstructor for the long input-delayed plant is established. The long dead time of interest is an integer plus a fractional input delay. An illustrative example is given to demonstrate the effective of the proposed approach.     

“信息科学基础”纵向关联与横向拓展教学研究

＂信息科学基础＂作为信息与计算科学专业开设的一门重要的专业基础课程,对于提高学生的信息科学基础知识具有重要的作用。针对在本专业开设该课程存在的主要问题,探讨该课程教学理念和教学方法中纵向关联与横向拓展的改革思路,切合实际提出一些新的教学方案,实践表明这些方法有效提高了信息论的教学效果。