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本文研究ARMA线性子系统串联分段线性函数的Wiener系统的递推辨识问题.利用相关分析法和Yule-Walker方程给出线性部分参数的递推辨识算法,而对非线性部分参数用递推的最小二乘(LS)算法给出估计,并证明了这些算法都以概率1收敛到真值. 相似文献
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系统辨识中参数估计的一致性问题已有很多研究。[1,2]研究了最小二乘辨识的弱一致性问题。[3,4]对离散时间系统、[5]对连续时间系统提出了保证最小二乘估计收敛且强一致的条件。但其中包含了噪声的条件协方差阵对(t,ω)一致有界。[6,7]把递推算法的收敛性、强一致性和某一常微分方程的稳定性建立了联系,这一类定理所讨论的并不是某一种特定的算法,而是一类算法。但[6]中所要求的条件很多,有的不容易验证,[7]中处理方法较[6]简单。但所要求的条件仍很强,特别是事先要求递推过程一致有界及常返某一紧集,这样一个不太合理的要求。 相似文献
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1.引言 对系统辨识中参数估计的一致性问题,已有很多研究,其中鞅和微分方程是两种较有成效的方法。[1,2]对离散时间系统,对连续时间系统分别用鞅的收敛性定理,证明了保证最小二乘估计收敛且一致的简单条件,但是这一类证明方法很难用到稍异于最小二乘的算法上去,并且还要求噪声的条件协方差阵对(t,ω)一致有界。[3,4]把递推算 相似文献
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为了提高人口预测精度,提出了基于多项式神经网络模型与递推最小二乘法的人口预测方法.方法完全避免了人为假设条件,充分利用我国六次人口普查数据来建立基于多项式神经网络模型的人口预测模型,并使用递推最小二乘算法递推计算多项式神经网络模型的加权系数.方法能有效预测中长期人口数据及其变化趋势.研究结果表明,中国将在2016年达到人口高峰1385亿. 相似文献
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研究了多输入多输出系统的状态空间模型的递推子空间辨识问题.针对只有输出量测噪声的线性时不变系统,提出了基于随机逼近-主成份分析(SA-PCA)的估计扩张能观矩阵的递推算法.同时利用递推最小二乘在线估计系统矩阵.最后通过仿真例子说明算法的收敛速度和估计效果. 相似文献
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至今为止,线性单变量系统的递推辨识已经有了许多有效的算法。相形之下,线性多变量系统的递推辨识有效算法要少的多。这些算法包括EL—Sherief和Sinha(1978)提出的递推最小二乘和随机逼近相结合的算法[1];Sinha和Kwong(1979)提出的广义最小二乘方法[2];Gauthier和Landau 相似文献
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等效系统参数辨识法在飞行品质评价中的应用 总被引:1,自引:0,他引:1
分析了等效系统参数辨识方法,采用最小二乘法与频域极大似然法求解先进飞机的低阶等效系统.通过计算,对两种辨识方法的优缺点进行了对比研究,并通过动态仿真验证了方法的有效性.最后依据参数辨识结果,对某型飞机的飞行品质进行了评估. 相似文献
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§1.引言 实l~2空间是由序列x=(x_0,x_1,…,x_n,…)组成的空间,其中x_i(i=0,1,…)是实数,x满足 相似文献
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Shaoqiang Tang 《偏微分方程(英文版)》1999,12(2):97-105
We study the time-periodic solutions to systems of conservation laws with ellipticity. It is shown that under time-periodic boundary condition, the system admits at least one global time-periodic solution bounded uniformly with the same period. 相似文献
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A hierarchical least squares (HLS) algorithm is derived in details for identifying MIMO ARX-like systems based on the hierarchical identification principle. It is shown that the parameter estimation errors by the HLS algorithm consistently converge to zero for bounded noise variances by using the stochastic martingale theory. A numerical example is given. 相似文献
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利用最小二乘法进行线性数据拟合在一定条件下存在着误差较大的缺陷,为使线性数据拟合方法在科学实验和工程实践中能够更加准确地求解量与量之间的关系表达式,本文通过对常用线性数据拟合方法———最小二乘法进行了误差分析,并在此基础上提出了最小距离平方和法以对最小二乘法作改进处理.最后,通过举例分析对两种线性数据拟合方法的优劣加以讨论并分别给出其较为合理的应用控制条件. 相似文献
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The inverse eigenvalue problem for a Sturm-Liouville equation in impedance form with Dirichlet boundary conditions on a unit interval is solved. The solution of this nonlinear problem requires the investigation of a combined map from the logarithmic derivative of the impedance, assumed to be square integrable, to two sequences of spectral data. The first is the sequence of Dirichlet eigenvalues, shown to be locally bounded with square roots differing from the sequence of integral multiples of π by a square summable sequence. The second sequence has as first term the mean of the logarithmic derivative of the impedance. Each term in the remainder of the sequence is the logarithm of the product of the impedance and the derivative of an eigenfunction evaluated at an endpoint. It is shown that this second sequence is a locally bounded square summable sequence. The combined map is a real analytic isomorphism. A uniqueness result follows from the asymptotics and analyticity shown in the first paper and properties of Riesz bases. The existence is shown by giving a closed form of the solution. It is also shown that the same map solves the inverse Sturm-Liouville problem in impedance form with Neumann boundary conditions. © 1993 John Wiley & Sons, Inc. 相似文献
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Coarse grid spaces for domains with a complicated boundary 总被引:1,自引:0,他引:1
Harry Yserentant 《Numerical Algorithms》1999,21(1-4):387-392
It is shown that, with homogeneous Dirichlet boundary conditions, the condition number of finite element discretization matrices
remains uniformly bounded independent of the size of the boundary elements provided that the size of the elements increases
with their distance to the boundary. This fact allows the construction of simple multigrid methods of optimal complexity for
domains of nearly arbitrary shape.
This revised version was published online in June 2006 with corrections to the Cover Date. 相似文献
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T. O. Shaposhnikova 《Journal of Mathematical Sciences》1988,42(2):1657-1665
It is shown that, under certain conditions, the bounded solutions of second-order linear elliptic differential equations are multipliers in certain weighted Hilbert spaces or in pairs of such spaces. Moreover, the role of the weight is played by a power of the distance to the boundary of the domain or by a function of the distance. This function is subjected to a condition which is necessary and sufficient for the solution to belong to the corresponding class of multipliers.Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 149, pp. 165–176, 1986. 相似文献
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On the explosive instability in a three‐species food chain model with modified Holling type IV functional response 下载免费PDF全文
Rana D. Parshad Ranjit Kumar Upadhyay Swati Mishra Satish Kumar Tiwari Swarnali Sharma 《Mathematical Methods in the Applied Sciences》2017,40(16):5707-5726
In earlier literature, a version of a classical three‐species food chain model, with modified Holling type IV functional response, is proposed. Results on the global boundedness of solutions to the model system under certain parametric restrictions are derived, and chaotic dynamics is shown. We prove that in fact the model possesses explosive instability, and solutions can explode/blow up in finite time, for certain initial conditions, even under the parametric restrictions of the literature. Furthermore, we derive the Hopf bifurcation criterion, route to chaos, and Turing bifurcation in case of the spatially explicit model. Lastly, we propose, analyze, and simulate a version of the model, incorporating gestation effect, via an appropriate time delay. The delayed model is shown to possess globally bounded solutions, for any initial condition. Copyright © 2017 John Wiley & Sons, Ltd. 相似文献
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对非线性参数规划问题$\varepsilon$-最优解集集值映射的连续性条件进行了研究.首先在可行集集值映射局部有界且正则的条件下,讨论了非线性参数规划问题最优值函数的连续性,然后针对$\varepsilon$-最优解集集值映射的结构特征并利用此结果和集值分析理论,给出了非线性参数规划问题$\varepsilon$-最优解集集值映射连续的一个充分条件. 相似文献
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M.J.D. Powell 《Numerische Mathematik》1994,68(1):107-128
Summary.
Let be a function from to that has
square
integrable second derivatives and let be the thin plate spline
interpolant
to at the points in
. We seek
bounds on the error when is in the convex
hull of
the interpolation points or when is close to at least one of
the
interpolation points but need not be in the convex hull. We find, for example,
that, if is inside a triangle whose vertices are any three
of the
interpolation points, then is bounded above by a
multiple of ,
where is the length of the longest side of the triangle and
where the
multiplier is independent of the interpolation points. Further, if
is any
bounded set in that is not a subset of a single straight
line, then we
prove that a sequence of thin plate spline interpolants converges to
uniformly on . Specifically, we require , where
is now the least upper bound on the numbers and where ,
, is
the least Euclidean
distance from to an interpolation point. Our method of
analysis applies
integration by parts and the Cauchy--Schwarz inequality to the scalar product
between second derivatives that occurs in the variational calculation of thin
plate spline interpolation.
Received November 10, 1993 / Revised version received March 1994 相似文献