基于δ法求解高阶时变非线性微分方程

该文基于二阶线性微分方程δ法绘制相平面原理,提出一种新颖而简单计算圆弧圆心和半径的方法实现高阶时变非线性微分方程相平面的作图,从而得到求解高阶时变非线性微分方程时域解的算法,并与龙格-库塔法等解析法相比具有计算简单、结果精度高的特点。     

面向非线性轨道车辆动力学的广义多步显式积分算法应用*

为了改善计算效率,在非线性轨道车辆动力学仿真中引入广义多步显式积分算法.针对非线性系统将算法改造为增量格式.列车动力学模型由轨道车辆模型和钩缓装置模型等组成.采用增量格式的广义多步显式积分算法分别研究列车连挂冲击和列车中低速碰撞问题.研究结果表明:广义多步显式积分算法在测试的算例中具有良好的稳定性,其计算速度约为龙格库塔法的3.8倍.干摩擦式钩缓装置模型在过渡状态存在车钩锁死现象.由于车钩锁死列车撞击过程中会出现车体加速度的高频振荡.广义多步显式积分算法可以适用于非线性轨道车辆动力学仿真.     

河流水质模型求解的Chebyshev正交多项式方法

提出一种考虑弥散时Streeter—Phelps一维稳态河流水质模型Chebyshev正交多项式的近似解法．通过对稳态河流水质模型的非线性高阶微分方程式分析,采用Chebyshev正交多项式对各阶微分和弥散系数D进行近似描述,得到稳态河流水质模型的近似表达式．针对近似模型给出了误差指标,并采用最小二乘对近似式中的未知参数进行估计;同时,对算法的总精度进行了讨论．仿真结果表明,该方法的精度高于多种微分方程数值计算方法(如龙格一库塔),不仅可以提高生化需氧量的计算精度,而且能够大大提高溶解氧浓度计算结果的准确性．     

一种基于时间差分算法的神经网络预测控制系统

为提高多步预测控制的计算效率，提出一种基于时间差分算法的Elman网络多步预测控制器的设计方法．用Elman网络对非线性系统输出值进行直接多步预估，并针对BP算法无法对网络权值的实时调整进行渐进计算的缺点，提出了将时间差分法和BP算法相结合的新的网络学习算法；为简化计算，采用单值预测控制算法对非线性系统进行滚动优化以实现对下一步控制量的优化计算．理论分析与仿真结果表明，该方法具有结构简单、运算量小、速度快的特点，可应用于实时快速系统，并且对系统参数的变化具有一定的自适应性．     

Lyapunov指数计算算法的设计与实现

为了定量分析混沌系统的动力学特性,论文研究了计算Lyapunov指数的Jacobi矩阵算法,并采用Matlab6.5软件平台设计了基于该算法的Lyapunov指数计算软件,算法程序简洁、可读性强、易于移植,GUI编程技术使人机交换能力增强,制作的Lyapunov指数工具箱能够求解非线性动力学系统的Lyapunov指数谱和分数维。最后,分析了迭代次数、计算步长、解法器和初值等因素对计算精度的影响。     

比较定理在非线性系统开关控制计算中的应用

多数实际物理系统都具有某种程度的非线性,因此需要寻求有关非线性系统简便有效的解法。本文的目的是说明如何通过对近似线性模型的研究,来实现非线性系统特性的区域划分,并着重说明对二阶模型开关控制问题的计算和实际应用。     

OFDM系统中一种新的非线性补偿算法

在频率选择性信道中,正交频分复用（OFDM）技术以其独特的优点得到了人们的青睐。但高峰均功率比（PAPR）,易使功率放大器（HPA）输出信号产生非线性失真。在OFDM系统中提出了一种新的非线性补偿算法,该算法利用导频序列估计发射端HPA参数,并由此计算非线性误差,实现非线性补偿。计算机仿真结果表明,该算法具有较好的补偿效果。     

函数依赖集在属性子集上投影新算法

分析了分解法分解关系模式在数据库设计应用中存在的问题是函数依赖集在属性子集上投影的计算问题，而后对该问题提出了解决的方法和技术，并设计了具体的算法。该算法为解决此计算问题提供了一个有效途径，给分解法分解关系模式在数据库设计中的应用创造了更有利条件。     

基于离散傅里叶变换的姿态算法研究

捷联惯性导航系统已经在航空航天的各个领域中获得了广泛应用.捷联惯性导航系统根据固定在载体上的陀螺仪输出的角度或者角速率信息实时计算载体相对于惯性参考系的姿态变换矩阵.为确保姿态实时计算精度,根据信号处理中信号重构的相关理论,利用角速率信息求解四元数姿态微分方程的离散傅里叶方法,并以典型圆锥运动作为输入条件对算法进行仿真.仿真结果表明,提出方法在高动态角运动环境下的解算精度要优于四阶龙格库塔算法,由圆锥运动引起的俯仰角算法漂移误差也要小于四阶龙格库塔方法.     

随机共振数值仿真的快速算法

根据信噪比曲线可以判断一个非线性系统是否发生随机共振,同时也可以得到非线性系统对噪声的输出性能。然而,由于要进行系综平均,即使要得到最简单的双稳态系统的信噪比曲线也需要很长时间的运算。经过对双稳态系统产生随机共振过程的仔细分析,以龙格—库塔法为基础,利用适当的数值计算方法,可以快速地求解双稳态系统的输出。     

An approximate solution to an initial boundary value problem: Rakib–Sivashinsky equation

The construction of an approximate solution to an initial boundary value problem for the Rakib–Sivashinsky equation is of concern. The Fourier method is combined with the Adomian decomposition method in order to provide the approximate solution. The variables are separated by the Fourier method and the approximate solution to the nonlinear system of ordinary differential equations is obtained by the Adomian decomposition method. One example of application is presented.     

Improved Adomian decomposition method

In this paper a new treatment for the Adomian decomposition method (ADM) is introduced. The new treatment is called the improved Adomian decomposition method (IADM) which improves the results obtained from the known Adomian decomposition method. The improved Adomian decomposition method is applied for the analytic treatment of nonlinear initial value problems. The improved method accelerates the convergence of the series solution, and provides the exact power series solution. It solves the drawbacks in the standard Adomian decomposition method.     

Determination of a time-dependent parameter in a one-dimensional quasi-linear parabolic equation with temperature overspecification

In this work, the Adomian decomposition method is used to find the solution to a one-dimensional quasi-linear parabolic partial differential equation with a time-dependent unknown function. A wide class of physical phenomena is modelled by non-classical parabolic initial-boundary value problems. Thus the theoretical behaviour and numerical approximation of these problems have been active areas of research. The decomposition procedure first proposed by the American mathematician G. Adomian (1923–1996) is useful for obtaining both exact solutions to, and numerical approximations of, various kinds of linear and nonlinear problem. The Adomian decomposition method, which accurately computes the series solution, is of great interest in science and engineering. It provides a solution as a convergent series with components that can be elegantly computed. Sufficient conditions for convergence and stability of the approximate solution are given and the results of numerical experiments are presented.     

The solution of a nonclassic problem for one-dimensional hyperbolic equation using the decomposition procedure

In this article, we propose a new approach for solving an initial–boundary value problem with a non-classic condition for the one-dimensional wave equation. Our approach depends mainly on Adomian's technique. We will deal here with new type of nonlocal boundary value problems that are the solution of hyperbolic partial differential equations with a non-standard boundary specification. The decomposition method of G. Adomian can be an effective scheme to obtain the analytical and approximate solutions. This new approach provides immediate and visible symbolic terms of analytic solution as well as numerical approximate solution to both linear and nonlinear problems without linearization. The Adomian's method establishes symbolic and approximate solutions by using the decomposition procedure. This technique is useful for obtaining both analytical and numerical approximations of linear and nonlinear differential equations and it is also quite straightforward to write computer code. In comparison to traditional procedures, the series-based technique of the Adomian decomposition technique is shown to evaluate solutions accurately and efficiently. The method is very reliable and effective that provides the solution in terms of rapid convergent series. Several examples are tested to support our study.     

基于双线性模型的动态系统优化和参数估计集成方法

针对双线性模型与实际系统之间的差异，提出一种基于双线性模型求解非线性动态系统最优控制的迭代算法。该算法通过重复求解修正的基于双线性模型的优化控制问题和参数估计问题，获得实际系统的最优解。同时提出求解修正的基于双线性模型的优化控制问题的一种新的分解方法，克服了非线性和双线性两点边值问题求解的困难。仿真例子表明该算法的有效性和实用性。     

加权有向图社区发现的子系统划分

提出一种基于加权有向图的社区发现子系统划分方法, 并应用于分布式状态估计设计. 针对一类复杂非线 性系统, 构建考虑连接边强度的加权有向图, 引入社区发现算法将复杂非线性系统划分成多个子系统. 同时考虑子 系统之间连接边的数量和有向图顶点之间的连接强度, 使得划分得到的子系统内部关联较强, 而子系统之间的耦合 强度较弱. 针对划分得到的子系统, 设计基于信息交互的分布式滚动时域估计算法, 并与已有的子系统划分方法对 比, 在相同的状态估计设定下, 所提出的子系统划分方法能够有效提高状态估计的性能.     

An expert system based on wavelet decomposition and neural network for modeling Chua’s circuit

This paper presents an expert system based on wavelet decomposition and neural network for modeling and simulation of Chua’s circuit which is used for chaos studies. The problems which arise in modeling Chua’s circuit by neural networks are high structural complexity and slow and difficult training. With this proposed method a new solutions is produced to solve these problems. Wavelet decomposition is used for new useful feature extracting from input signal and neural network is used for modeling. Test results of proposed wavelet decomposition and neural network model are compared with test results of neural network model. Desired performance is provided by this new model. Test results showed that the suggested method can be used efficiently for modeling nonlinear dynamical systems.     

A New Approach to the Gas Dynamics Equation: An Application of the Decomposition Method

The Adomian decomposition method is used to implement the homogeneous gas dynamics equations. The analytic solution of the equation is calculated in the form of a series with easily computable components. The homogeneous problem is quickly solved by observing the self-canceling "noise" terms whose sum vanishes in the limit. Comparing the methodology with some other known techniques shows that the present approach is effective and powerful. Many test modeling problems from mathematical physics, both linear and nonlinear are discussed to illustrate the effectiveness and the performance of the decomposition method.     

非线性控制系统与状态空间的几何结构

首行从整体化的观点定义了一种建立在黎曼流形上的非线性控制系统,给出了系统的状态方程在黎曼流形的局部坐标系下的表达式,讨论了黎曼流形的几何结构对非线性系统的影响,研究了非线性系统的能控性和能观测性,其次,利用对合分布与全测地子流形的性质,给出了建立在黎曼流形上的非线性系统的局部能控结构分解,局部能观结构分解和Kalman分解,第三,分别利用彼此正交的对合分布族和递增对合分布族与全测地子流形族的性质。研究了建立在黎曼流形上的非线性控制系统平等解耦问题和级联解耦问题,以及仿射非线性控制系统的局部干扰解耦问题。     

Estimates of the solution set of nonlinear equations with uncertain parameters

We consider the problem of determining the entire solution set of a system of nonlinear equations with interval coefficients. A decomposition method is proposed which produces an upper estimate of the sought solution as the union of convex sets. A numerical simulation example is described.Translated from Kibernetika, No. 5, pp. 38–43, 54, September–October, 1990.