超混沌系统的函数投影同步与参数辨识

研究了一参数未知超混沌系统的函数投影同步问题．基于李雅谱诺夫稳定性理论,设计了实现混沌系统函数投影同步的有效非线性控制器,可以快速实现超混沌系统的加速函数投影同步,同时设计了参数控制律,有效的辨识了系统的未知参数,数值仿真验证了理论分析和数值计算的正确性．     

线性过程误差下的非参数回归模型的注记

对于非参数回归模型Yni=g(xni)+εni,1in,用一般非参数方法,定义了未知函数g(.)的估计量gn(x),当误差序列{εni,1in}为一弱平稳线性过程序列时,在一定条件下,获得了估计量gn(x)的一致强相合性.     

以函数为参量的间歇发酵非线性动力系统及其辨识

建立以连续分段线性函数为参量的间歇发酵非线性动力系统,证明该动力系统的主要性质及解的存在性.以实验数据拟合得到的光滑曲线为依据,提出了连续分段线性函数为优化变量的辨识模型,论述可辨识性.依状态变量与辨识函数的相关性,构造求解辨识模型的优化算法,并给出优化算法的收敛性分析及数值结果.     

几类典型随机非线性系统的辨识

考察实际中常见的三类典型随机非线性系统(即Wiener、Hammerstein和NARX系统)的辨识,首先概述了现有的递推和非递推辨识算法,然后介绍这三类系统的一个统一辨识框架:利用系统所确定的过程的马氏性及混合型,将辨识转化为求函数零点的问题,基于扩张截尾的随机逼近算法,得到了递推、强一致的辨识结果,并给出了数值模拟验证辨识算法收敛到真值.     

基于指数矩鞅差序列非参数回归函数的估计

本文研究了误差项是鞅差序列,且满足某种指数矩条件的非参数回归函数的估计.利用鞅的某种指数不等式,得到了其加权核估计的强相合以及在有限闭区间内一致强相合的性质,并在某种意义上推广了[5]的结果.     

分段线性非线性汽车悬架系统的分岔行为

建立了由主、副簧组成的分段线性非线性悬架系统动力学模型,应用奇异性理论研究了两个自由度汽车悬架系统共振解的分岔,得到系统的转迁集和40组分岔图,发现了非常复杂的局部分岔,分岔图全面展示了这一系统的分岔特性.由系统参数与该系统的拓扑分岔解之间的联系,分析并得到了不同参数下系统的运动特性,为实现悬架参数的优化控制提供了理论依据.     

分布参数系统辨识的必要条件(英文)

考虑了辨识下列方程中算子值参数Ｂ的必要条件,代价泛函为：证明了：最佳估计Ｂ０由一个优化系统确定,而该优化系统由状态方程、伴随方程和优化条件组成．     

核实数据下误差为鞅差序列的部分线性模型的估计及性质

Consider the partly linear model Y = xβ + g(t) + e where the explanatory x is erroneously measured,and both t and the response Y are measured exactly,the random error e is a martingale difference sequence.Let x be a surrogate variable observed instead of the true x in the primary survey data.Assume that in addition to the primary data set containing N observations of {(Y_j,x_j,t_j)_(j=n+1)~(n+N),the independent validation data containing n observations of {(x_j,x_j,t_j)_(j=1)~n} is available.In this paper,a semiparametric method with the primary data is employed to obtain the estimator of β and g(·) based on the least squares criterion with the help of validation data.The proposed estimators are proved to be strongly consistent.Finite sample behavior of the estimators is investigated via simulations too.     

半参数回归模型小波估计的强相合性

考虑半参数回归模型y_i~(n)=X_i~((n)T)β+g(t_i~(n))+ε_i~(n)(1■i■n),其中β∈R~d为未知参数,g(t)为[0,1】上的未知Borel函数,X_i~(n)为R~d上的随机设计,随机误差序列{ε_i~(n)}为鞅差序列,{t_i~(n))为[0,1]上的常数序列．本文用小波的方法得到β、g(t)的估计量分别为■_n、■_n(t),并证明了它们的强相合性．     

多元线性模型中的一个参数函数的UMVIQUE的存在性

考虑多元线性模型 Y=X_1BX＇_2 Uε,Eε=0,其中ε=（ε_1,…,ε_n）＇,ε==(ε_1',...ε_n'),E(εε)=I（×）∑,∑≥0。是未知协差阵。本文给出了tr（C∑）的一致最小方差不变二次无偏估计（简记为UMVIQUE）存在的充要条件。     

Identification of a Discontinuous Parameter in Stochastic Parabolic Systems

The purpose of this paper is to study the identification problem for a spatially varying discontinuous parameter in stochastic diffusion equations. The consistency property of the maximum likelihood estimate (M.L.E.) and a generating algorithm for M.L.E. have been explored under the condition that the unknown parameter is in a sufficiently regular space with respect to spatial variables. In order to prove the consistency property of the M.L.E. for a discontinuous diffusion coefficient, we use the method of sieves, i.e., first the admissible class of unknown parameters is projected into a finite-dimensional space and next the convergence of the derived finite-dimensional M.L.E. to the infinite-dimensional M.L.E. is justified under some conditions. An iterative algorithm for generating the M.L.E. is also proposed with two numerical examples. Accepted 2 April 1996     

具间断系数线性双曲型方程组

考虑具间断系数线性双曲型方程组Riemann问题,利用分析的方法证明了该问题包含δ波解的存在性.     

Optimal Discontinuous Feedback Controls for Linear Systems

The synthesis of optimal feedback controls for linear systemswith constrained inputs is studied. An integral cost is minimized,the integrand being the sum of a quadratic state penalty term,a fuel-type control penalty term, and a nonquadratic functionof the state. The latter function is regarded as a problem-regularizingterm which is chosen so as to admit a simple explicit feedbackcharacterisation of the optimal control. Formulations with anonautonomous finite time interval and an autonomous semi-infinitetime horizon are treated, and an example of each type of problemis presented.     

Stability of Linear Parameter Varying and Linear Switching Systems

We consider stability of families of linear time‐varying systems, that are determined by a set of time‐varying parameters which adhere to certain rules. The conditions are general enough to encompass on the one hand stability questions for systems that are frequently called linear parameter varying systems in the literature and on the other hand also linear switching systems, in which parameter variations are allowed to have discontinuities. Combinations of these two sets of assumptions are also possible within the framework studied here. Under the assumption of irreducibility of the sets of system matrices, we show how to construct parameter dependent Lyapunov functions for the systems under consideration that exactly characterize the exponential growth rate. It is clear that such Lyapunov functions do not exist in general. But every system of our class can be reduced to a finite number of subsystems for which irreducibility holds.     

Sequential Identification of Linear Dynamic Systems with Memory

This paper presents a sequential estimator for some unknown parameters in stochastic linear systems with memory. As examples stochastic differential equations with time delayed drift are considered. Based on the maximum likelihood method, we construct an estimation procedure with given accuracy in the sense of the L _p -norm (p 2). It is shown, that this procedure works also in certain cases, when the normalized information matrix of the observed process is asymptotically degenerated. The almost surely consistency of the proposed estimators and the asymptotic behavior of the length of observations are derived.     

Identification of Linear Error-Models with Projected Dynamical Systems

Linear error models are an integral part of several parameter identification methods for feedforward and feedback control systems and lead in connection with the L ₂-norm to a convex distance measure which has to be minimised for identification purposes. The parameters are hereby often subject to specific restrictions whose intersections span a convex solution set with non-differentiability points on its boundary. For solving these well conditioned problems on-line the paper formulates the solution of the bounded convex minimisation problem as a stable equilibrium set of a proper system of differential equations. The vector field of the corresponding system of differential equations is based on a projection of the negative gradient of the distance measure. A general drawback of this approach is the discontinuous right-hand side of the differential equation caused by the projection transformation. The consequence are difficulties for the verification of the existence, uniqueness and stability of a solution trajectory. Therefore the first subject of this paper is the derivation of an alternative formulation of the projected dynamical system, which exhibits, in contrast to the original formulation, a continuous right-hand side and is thus accessible to conventional analysis methods. For this purpose the multi-dimensional stop operator is used and the existence, uniqueness and stability properties of the solution trajectories are established. The second part of this paper deals with the numerical integration of the projected dynamical system which is used for an implementation of the identification method on a digital signal processor for example. To demonstrate the performance the application of this on-line identification method to the hysteretic filter synthesis with the modified Prandtl-Ishlinskii approach is presented in the last part of this paper.     

Description of the Structure of Irregularity Sets of Linear Differential Systems with a Linear Parameter

Differential Equations - We consider the class of linear parametric differential systems $$\dot {x}=\mu A(t)x $$ defined on the half-line $$t\geq 0 $$ , where $$\mu \in \mathbb {R} $$ is a...     

不连续系统有界变差解对参数的连续依赖性

利用Henstock积分，讨论了一类不连续系统有界变差解对参数的连续依赖性及其它相关性质．     

An Approach for Parameter Identification in Distributed Parameter Systems

Identification of physical parameters in systems modelled by linear partial differential equations (p.d.e.) from lumped measurements is considered. The problem is solved by means of an alternative formulation of the boundary value problem as convolutional system. The approach allows for the identification even in the presence of non-homogeneous initial conditions. (© 2012 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)