一类线性系统求解的并行算法

本文给出了求解块角结构的大线性系统的一种并行算法 .这一方法以“梯度—单纯形”法为基础 ,将大线性问题分解为若干子线性系统 ,通过并行地对各个子系统求解 ,求得大系统的最优解 .该算法提高了大系统求解速度 ,特别适合于耦合约束较少的大线性问题 .本文还对该算法的应用性进行了分析.     

动态矩阵解耦控制及其应用

针对双输入双输出的多变量强耦合系统，首先将其分解为两个双输入单输出系统，并用动态矩阵控制原理设计了控制器。通过求解二元一次矩阵方程组，实现了多步预测的解耦控制。仿真研究结果证实了该算法的有效性。     

奇异摄动理论

本文介绍了奇异摄动法在线性控制系统中的应用。利用这一方法可以将一个高阶系统的求解分为两个低阶系统分别求解问题,这样既可降低求解的系统阶次,又能克服系统方程组的刚性,从而大大减小计算量。因此它可用于控制系统的分析、综合和设计。文中对多重时间尺度模型、线性奇异摄动模型、利用逆变换的奇异摄动法、稳定性、可控性和可观测性、最佳线性调节器及最优线性控制等问题作了阐述。     

组合式复杂大系统优化的解耦方法

本文在分析了组合式复杂大系统特点的基础上，提出了这类系统求解的解耦方法，这一方法包含系统的分形，分形系统的求解和分形解的合成三部分，是这类系统求解的理想方法之一。     

序列ISAR像复杂结构航天器在轨姿态估计

针对“中国空间站”等复杂结构航天器在轨姿态估计误差精度优化的问题，提出了一种基于多线性结构特征优化选择的姿态估计方法。首先采用奇异值分解方法获取ISAR等效成像平面的空间位置，然后通过Unet3+神经网络分割出航天器的典型部件，进而获取各部件的线性结构，最后建立优化函数求解航天器在轨姿态角。仿真和实测实验结果表明，相比现有方法，所提方法能够实现结构特征的自动提取并有效减少姿态估计误差。     

改进的逆解耦自抗扰内模控制在磨矿中的应用

针对磨矿分级系统的多变量、强耦合、大时滞等特性,提出改进的逆解耦自抗扰内模控制方法。利用逆解耦方法实现磨矿分级系统的解耦,对解耦后的子系统采用改进的内模控制和线性自抗扰控制。通过引入内模补偿器和增益对时滞进行补偿,减小了系统对模型的依赖度,通过调节线性自抗扰控制器参数、内模补偿器参数和增益来抑制模型失配、外部干扰及不确定性因素对系统带来的不利影响。仿真结果表明,改进的逆解耦自抗扰内模控制方法有较好的解耦性能、跟踪性能和鲁棒性能,验证了此方法是有效的。     

基于递阶优化算法的一类两层规划问题的解法

提出一种基于分解协调的两级递阶结构优化算法来求解两层规划问题。通过设计解耦变量,两层规划问题被分解成若干相互独立的易于在结构的第一级求解的子问题。而结构的第二级是调整解耦变量使各子问题的解得以改善。算法以一种迭代的方式使第一级求得的子问题的解不断协调,最终达到两层规划的解。算例表明该算法是可行且有效的     

基于矩阵分解的惯导安装误差矩阵解耦方法

针对捷联惯性导航系统级标定中安装误差矩阵存在3组耦合关系问题,提出一种基于矩阵分解的解耦方法。该方法将安装误差矩阵分解为对称误差矩阵和斜对称误差矩阵后,推导其对惯性导航姿态方程和速度方程的影响,揭露系统级标定中安装误差矩阵存在耦合的原因——陀螺仪表组和加速度计仪表组的斜对称误差对误差方程的影响是耦合的,进而提出适当选取体坐标系使得陀螺仪表组的斜对称误差矩阵为0的解耦方法。该解耦方法是一种均值分配方法,与传统解耦方法相比能减少系统运算中的二阶舍项误差。仿真实例说明了该解耦方法是有效的。     

自校正解耦信息融合Wiener状态预报器

对含未知噪声方差阵的多传感器系统,用现代时间序列分析方法,基于滑动平均新息模型的在线辨识和求解相关函数矩阵方程组,可得到白噪声方差阵的在线估值器。在按状态分量标量加权线性最小方差最优信息融合准则下,提出了一种自校正解耦信息融合Wiener状态预报器,实现了状态分量的自校正解耦局部Wiener预报器和自校正解耦融合Wiener预报器。用动态误差系统稳定性分析方法证明了该预报器的收敛性,即若滑动平均新息模型参数估计是一致的,将收敛于噪声方差阵已知时的最优解耦信息融合Wiener状态预报器。一个带三传感器的目标跟踪系统的仿真例子说明了其有效性。     

动态解耦和变结构鲁棒补偿的导弹再入控制

导弹在大攻角再入飞行过程中,偏航通道和滚动通道存在着的气动交连耦合.采用动态解耦控制的方法,针对动态解耦对参数不确定性敏感这一缺点,提出了采用变结构鲁棒补偿控制的方法,使由于外来干扰和参数不确定性给解耦后的系统带来的残余耦合量衰减到一个适当的水平ρ,并获得一个H∞跟踪性能指标.理论分析和仿真结果表明,设计的控制系统对解耦后残余耦合进行了有效的衰减,并使系统具有良好的鲁棒性.     

B样条插值曲线的快速算法

６０年代以来，样条函数特别是Ｂ样条函数的理论有了很大发展，已经成为计算机辅助几何设计（ＣＡＧＤ）工作中的主要数学工具。在利用Ｂ样条函数构造插值曲线时，往往需要求解高阶线性方程组，给计算带来了一定困难。本文针对这一问题提出了一种快速算法，避免了对方程组的直接求解，从而简化了Ｂ样条插值曲线的计算。     

Novel method based on ant colony opti mization for solving ill-conditioned linear systems of equations

1 .INTRODUCTIONStudies have shownthat some systems are highlysen-sitive :a small perturbationin the data can result in alarge changeinthe solutions .Such systems are calledill-conditioned systems .Ill-conditionedlinear systemsof equations have a wide application in many fieldssuch asi magine processing,deconvolution, model pa-rameters esti mation.Because the condition number ofill-conditionedlinear systems of equationsis very big,the data error andthe rounding error inthe computa-tional p…     

B-spline patches and transfinite interpolation method for PDE controlled simulation

This paper is to discuss an approach which combines B-spline patches and transfinite interpolation to establish a linear algebraic system for solving partial differential equations and modify the WEB-spline method developed by Klaus Hollig to derive this new idea.First of all,the authors replace the R-function method with transfinite interpolation to build a function which vanishes on boundaries. Secondly,the authors simulate the partial differential equation by directly applying differential operators to basis functions,which is similar to the RBF method rather than Hollig’s method.These new strategies then make the constructing of bases and the linear system much more straightforward.And as the interpolation is brought in,the design of schemes for solving practical PDEs can be more flexible. This new method is easy to carry out and suitable for simulations in the fields such as graphics to achieve rapid rendering.Especially when the specified precision is not very high,this method performs much faster than WEB-spline method.     

THE POLE ASSIGNMENT OF LINEAR SYSTEMS

In this paper the pole assignment problem of a time invariant linear control system issolved by using the Wu Elimination Method.In general,the questions are classified into(i)the poleassignment by using state feedback,(ii)the pole assignment by using output feedback,(iii)the poleassignment via dynamic compensator.The key point of all these problems is to solve a certaincorresponding system of polynomial equations.Based on algebraic geometry,the Wu methodprovides a mechanical algorithm for solving the system of polynomial equations.Therefore,a unifieddefinite algorithm for solving all these problems is given in this paper.During the procedure ofelimination,the unknowns are automatically separated into parameters and apparent variables.Thus,the freedom of the corresponding feedback can be defined as the number of parameters.Meanwhile,the explicit expressions of the apparent variables depending on the parameters areobtained.     

基于Shifted Legendre正交多项式的迭代学习控制方法

考虑用迭代学习控制方法来解决一类线性时变连续系统的终端控制问题。运用ShiftedLegendre正交多项式的展开技术,利用其正交性和边值条件,将线性时变系统的微分方程转化为代数方程,避免了在判断误差收敛条件的过程中求解线性时变系统状态转移矩阵。并采用高阶学习律来求控制输入的ShiftedLegendre系数向量,仿真实例验证了该方法的有效性。     

求解非线性方程组的异步并行 拟牛顿迭代算法的收敛性分析

本文给出了MIMD多处理机上的求解非线性方程组的异步并行拟牛顿迭代算法的收敛性分析,给出了收敛的充分性条件。     

On the Solutions of the Matrix Equations in Optimal Stochastic Control

1.INTRoDUCTIoNoFTHEPRoBLEMConsiderthetime-invariantlinearIt6stochasticsystemwherexER,uCRm,FER""",BER""m,a=const.(i=1,2,'',k)arenaturalnumbers;W(t)=[W(t),W2(t),Wk(t)]"(tSo)isak-dimensionalstandardWienerprocesswithindependentcomponentsdefinedonthecompleteprobabilityspace(fl,FP),(A,B)iscontrollable.SupposethatRERm"m,QERmxmaregivenpositivedefiniteweightingmatrices,Ereferstothemathematicalexpectation.ConsidertheoptimalstochasticcontrolDroblemItiswell-knownthatifthereisapositive…     

Some Equivalence Transform Methods for Simulating Models in Control Systems

In this paper two classes of equivalence transform methods for solving ordinary differential equations are proposed. One class of method is the equivalence integral transform method for special differential algebraic problems. The advantage of this class of method is such that the amount of work calculating one integration with parameters becomes that of two interpolations, when the system of nonlinear equations is solved on the right hand side function. The other class of method is the equivalence substitution method tor avoiding calculating derivative on the right hand side function. In order to avoid calculation derivatives, two equivalence substitution methods are proposed here. The application instances of some special effect of the equivalence substitution methods are given.     

分数微积分的两种系统建模方法

介绍了Riemann-Liouville和Caputo分数微积分的定义及其部分性质。给出了分数阶线性定常微分方程的一般定义形式,并指出它是整数阶线性定常微分方程的推广。给出分数阶线性定常系统的传递函数和状态方程描述,并与整数阶线性定常系统的传递函数和状态方程作一比较,指出它们的异同点。运用拉普拉斯变换推导出其两种求解方法:直接求解法和状态空间法。最后给出一个实例说明这两种方法的有效性。     

Computer-aided design of classical linear compensators with application to aerospace

A new Matlab function based on a versatile compensator design approach is developed. This function allows design of lead-lag, PID, proportional plus rate feedback, proportional-integral plus rate feedback, and nth order linear compensators. The primary inputs to this function are the plant transfer function and the desired closedloop behavior in terms of an nth order transfer function. The output is the particular compensator parameters. The unified design approach is primarily based on minimizing a mean-squared error type objective function. This minimization gives the compensator parameters in terms of a set of linear simultaneous algebraic equations. This solution method requires the user to input such parameters as the lower and upper limits of frequency range of interest; such parameters are automatically determined by the use of numerical optimization. The design method and the associated software are demonstrated by solving a flexible satellite problem, and the results are compared with those obtained by two other methods reported in the open literatures.