Pointwise Stabilization for a Chain of Coupled Vibrating Strings

For the system representing a chain of coupled vibrating strings,we show that the associated semigroup satisfies the assumptionof spectrum-determined growth, and hence obtain conditions forenergy to decay strongly or exponentially. We examine in detailthe three-string case, and our results include those obtainedby others for the two-string case. Permanent address: Beijing Institute of Information and Control,Beijing, China.     

树状结构的弹性振动弦的节点反馈镇定

考虑树状结构的弹性振动弦网络系统．运用频域上的能量乘子法证明了当根部固定时，其余节点的线性反馈控制可使得系统能量指数衰减且谱确定增长条件成立．     

On the Enumeration of Non-Crossing Pairings of Well-Balanced Binary Strings

A non-crossing pairing on a binary string pairs ones and zeroes such that the arcs representing the pairings are non-crossing. A binary string is well-balanced if it is of the form ${1^{a_1} 0^{a_1}1^{a_2} 0^{a_2} . . .1^{a_r} 0^{a_r}}$ . In this paper we establish connections between non-crossing pairings of well-balanced binary strings and various lattice paths in plane. We show that for well-balanced binary strings with a ₁ ≤ a ₂ ≤  . . . ≤  a _r , the number of non-crossing pairings is equal to the number of lattice paths on the plane with certain right boundary, and hence can be enumerated by differential Goncarov polynomials. For the regular binary strings S =  (1 ^k 0 ^k ) ⁿ , the number of non-crossing pairings is given by the (k + 1)-Catalan numbers. We present a simple bijective proof for this case.     

Forecasting for Stationary Binary Time Series

The forecasting problem for a stationary and ergodic binary time series {X _n } _n=0 is to estimate the probability that X _n+1=1 based on the observations X _i , 0in without prior knowledge of the distribution of the process {X _n }. It is known that this is not possible if one estimates at all values of n. We present a simple procedure which will attempt to make such a prediction infinitely often at carefully selected stopping times chosen by the algorithm. We show that the proposed procedure is consistent under certain conditions, and we estimate the growth rate of the stopping times.     

随机时滞控制系统的均方BIBO稳定性

本文研究了具有时滞和非线性扰动的随机控制系统的均方有界输入-有界输出(BIBO)稳定.首先,探讨了具有离散时滞和非线性扰动的随机系统的均方BIBO稳定性问题,在此基础上,进一步研究带有离散时滞和分布时滞以及非线性扰动的随机系统的均方BIBO稳定性.通过设计合理的控制器,建立合适的Lyapunov泛函,结合Riccati矩阵方程,得到时滞依赖的均方BIBO稳定性条件.     

时滞广义时变系统的容许性分析与镇定

研究了时滞广义时变系统的容许性与镇定性问题.首先,基于广义Lyapunov不等式、线性矩阵不等式和受限等价方法,建立时滞广义时变系统的Lyapunov不等式,将时滞广义时变系统的容许性问题转化为求解时滞广义时变系统的Lyapunov不等式问题,得到了系统容许的充分条件.然后,根据充分条件进一步研究了时滞广义时变系统的镇定问题,给出了状态反馈镇定器的设计方法.最后,通过数值算例验证了所得结论的有效性.     

一类具有零动态不确定非线性系统的有限时间镇定问题

研究了一类带有零动态不确定非线性系统的有限时间镇定问题.基于有限时间稳定的Lyapunov理论和反推技术给出了一个状态反馈控制器的设计步骤,解决了这类不确定非线性系统的有限时间镇定问题.     

中立型时变非线性控制系统的镇定与控制

本文利用［１－ ３］中的方法,讨论了一类具有滞后的中立型时变非线性控制系统（在闭环情况下）的镇定与次优控制问题．得到了滞后量与非线性项的估计范围．     

Random Motion of Strings and Related Stochastic Evolution Equations with Monotone Nonlinearities

Abstract

A limiting problem for a stochastic evolution equation is studied in the paper. In the equation, the linear operator is non-positive with a pure point spectrum, the non-linearity is monotone, and the Brownian motion is cylindrical. It is shown that, in the limit, the mild solution to the evolution equation tends to the solution of an ordinary Ito equation.     

Statistical Estimation of Parameters for Binary Conditionally Nonlinear Autoregressive Time Series

The problem of statistical parameter estimation is considered for binary GLM-based autoregression with the link function of general form and the base functions (regressors) nonlinear w.r.t. the lagged variables. A new consistent asymptotically normal frequencies-based estimator (FBE) is constructed and compared with the classical MLE. It is shown that the FBE has less restrictive sufficient conditions of uniqueness than the MLE (does not need log-concavity of the inverse link) and can be computed recursively under the model extension. The sparse version of the FBE is proposed and the optimal model-dependent weight matrices (parameterizing the FBE) are found for the FBE and for the sparse FBE. The proposed empirical choice of the subset of s-tuples for the sparse FBE is examined by numerical and analytical examples. Computer experiments for comparison of the FBE versus the MLE are performed on simulated and real (genetic) data.     

一类高阶非线性系统停息时间可调的有限时间镇定

研究了一类高阶非线性系统停息时间可调的有限时间稳定性分析与控制器设计问题.利用有限时间Lyapunov定理的反步构造法,设计状态反馈有限时间控制器,并实现停息时间的适当调整.     

Small Time Asymptotics for Stochastic Evolution Equations

We obtain a large deviation principle describing the small time asymptotics of the solution of a stochastic evolution equation with multiplicative noise. Our assumptions are a condition on the linear drift operator that is satisfied by generators of analytic semigroups and Lipschitz continuity of the nonlinear coefficient functions. Methods originally used by Peszat (Probab. Theory Relat. Fields 98:113?C136, 1994) for the small noise asymptotics problem are adapted to solve the small time asymptotics problem. The results obtained in this way improve on some results of Zhang (Ann. Probab. 28(2):537?C557, 2000).     

Ostrowski Type Inequalities on Time Scales for Double Integrals

In this paper we first derive an Ostrowski type inequality on time scales for double integrals via ΔΔ-integral which unify corresponding continuous and discrete versions. We then replace the ΔΔ-integral by the ∇ ∇-, Δ∇-, and ∇Δ-integrals and get completely analogous results.     

Ostrowski Type Inequality for Double Integrals on Time Scales

We prove the Ostrowski type inequality for double integrals on time scales and thus unify corresponding continuous and discrete versions from the literature. We also apply the Ostrowski inequality for double integrals to the quantum time scales.     

一类非线性时滞系统的时滞相关镇定及跟踪控制问题

本文讨论了一类满足Lipschitz条件的非线性时滞系统的镇定与跟踪控制问题.基于非线性状态反馈控制器,利用Lyapunov-Krasovskii泛函和矩阵理论,得到了系统时滞相关全局渐近镇定的新判据,并且保证了输出和状态跟踪控制的误差全局渐近收敛于零.本文推广了文献[9]所得到的结论.因此,本文所研究的模型及所给出的判定条件更具有一般性和实用性.     

Algebraic Approach to the Stabilization of a Differential System of Retarded Type

For a spectrally controllable linear autonomous systems with commensurable delays, we construct state feedbacks ensuring the complete damping of the original system (finite stabilization) as well as the complete damping of the original system and the asymptotic stability of the closed-loop system (complete stabilization). The spectral reduction and asymptotic stabilization problems are considered as auxiliary problems. The argument is constructive, and the results are illustrated by an example.     

Evolution Systems for Differential Equations with Variable Time Lags

We consider nonautonomous retarded functional differential equations under hypotheses which are designed for the application to equations with variable time lags, which may be unbounded, and construct an evolution system of solution operators which are continuously differentiable. These operators are defined on manifolds of continuously differentiable functions. The results apply to pantograph equations and to nonlinear Volterra integro-differential equations, for example. For linear equations we also provide a simpler evolution system with solution operators on a Banach space of continuous functions.     

发展型方程的时间间断时空有限元方法

时空有限元方法通过统一时间和空间变量,克服了传统有限元方法对时间作差分离散引起的时间上的低精度,不但具有时、空高精度,而且在无结构网格上耗散特性好、无条件稳定,成为解决时间依赖问题的有效方法.本文利用抛物问题给出时间允许间断而空间连续的时空有限元方法的基本概念和过程,给出抛物型方程、积分-微分方程、双曲方程、Sobolev方程和其他高阶方程的算例,验证方法的精度和稳定性,并综合评价时间间断时空有限元方法目前的发展现状和应用前景.     

分数阶微分中立型系统的有限时间镇定性及有界性

讨论了一类分数阶微分中立型系统的有限时间状态反馈镇定性及有界性问题.利用Gronwall 不等式, 获得了使得系统有限时间状态反馈镇定及有限时间有界的充分性条件.