Regulator problem for uncertain linear discrete-time systems with constrained control

A necessary and sufficient condition to test the robustness of a regulator of uncertain linear systems with constrained control is given. The candidate regulator for this test is that stabilizing nominal systems. An illustrative example is also given.     

On a three-dimensional axisymmetric boundary-value problem of nonlinear elastic deformation: Asymptotic solution and exponentially small error

In this paper, we study a three-dimensional axisymmetric boundary-value problem of a slender cylinder composed of a nonlinearly elastic material subjected to an axial force. Starting from the field equations, after a transformation and proper scalings, we identify a small variable and two small parameters, which characterize the present problem. Then, by an approach involving compound series-asymptotic expansions, a nonlinear ODE is derived, which governs the axial strain (the first-term in the series expansion). By imposing the zero radial displacement conditions at two ends, we manage to get the analytical solution of the axial strain, from which all other physical quantities can be deduced and thus the three-dimensional displacement field can be determined. Graphical results are presented, which show that there are two boundary layers near the two ends while the middle part is in a state of almost uniform extension. The asymptotic structure of the analytical solution is derived, which offers clear explanations to the structure of the deformed configuration and shows that the thickness of both boundary layers is of the order of the radius. We also point out the relevance of the present results to the St. Venant’s problem. In particular, we obtain the explicit uniformly-valid exponentially small error term, when the obtained deformed configuration is compared to the configuration of a uniform extension.     

SPECTRAL DENSITY ESTIMATION FROM NONLINEARLY OBSERVED DATA

Abstract. The estimation of the spectral density function of a stationary Gaussian process at the input of an instantaneous nonlinearity is considered when the nonlinearity is known and a finite set of observations of the output process is given. A class of spectral estimates is considered and their quadratic-mean consistency is established; precise asymptotic expressions for their bias and covariance are derived and their asymptotic normality is obtained.     

保序回归的大样本性质

利用保序回归与极大似然估计之间的关系,从极大似然估计解的大样本性质出发,得到了保序回归解的两个大样本性质。     

基于约束优化的联想记忆模型学习算法

本文提出了一种对称互连神经元网络的学习策略,利用全局约束优化方法确定连接权。优化过程采用了梯度下降技术。这种学习算法可以保证训练样本成为系统的稳定吸引子,并且具有优化意义上的最大吸引域。本文讨论了网络的存储容量,训练样本的渐近稳定性和吸引域大小。计算机实验结果说明了学习算法的优越性。     

相关噪声中随机信号的Robust检测

本文重点讨论了在平稳ｍ相依噪声中弱随机信号的最佳无记忆Ｒｏｂｕｓｔ检测问题；并且以渐近功效函数为测度准则得到了最大最小无记忆非线性Ｒｏｂｕｓｔ检测器。     

Self-controlled case series analyses: Small-sample performance

Second-order expressions for the asymptotic bias and variance of the log relative incidence estimator are derived for the self-controlled case series model in a simplified scenario. The dependence of the bias and variance on factors such as the relative incidence and ratio of risk to observation period are studied. Small-sample performance of the estimator in realistic scenarios is investigated using simulations. It is found that, in scenarios likely to arise in practice, asymptotic methods are valid for numbers of cases in excess of 20-50 depending on the ratio of the risk period to the observation period and on the relative incidence. The application of Monte Carlo methods to self-controlled case series analyses is also discussed.     

An algorithm for the three-dimensional packing problem with asymptotic performance analysis

The three-dimensional packing problem can be stated as follows. Given a list of boxes, each with a given length, width, and height, the problem is to pack these boxes into a rectangular box of fixed-size bottom and unbounded height, so that the height of this packing is minimized. The boxes have to be packed orthogonally and oriented in all three dimensions. We present an approximation algorithm for this problem and show that its asymptotic performance bound is between 2.5 and 2.67. This result answers a question raised by Li and Cheng [5] about the existence of an algorithm for this problem with an asymptotic performance bound less than 2.89. This research was partially supported by FAPESP (proc. 93/0603-1) and by CNPq/ProTeM-CC, project ProComb (proc. 680065/94-6).     

Stability of Impulsive Stochastic Neutral Partial Differential Equations With Infinite Delays

In this paper, we study the existence and asymptotic stability in the pth moment of the mild solutions to impulsive stochastic neutral partial differential equations with infinite delays. Sufficient conditions ensuring the stability of the impulsive stochastic system are established. The results are obtained via the Banach fixed point theorem.     

Estimation in Random Coefficient Autoregressive Models

Abstract. We propose the quasi‐maximum likelihood method to estimate the parameters of an RCA(1) process, i.e. a random coefficient autoregressive time series of order 1. The strong consistency and the asymptotic normality of the estimators are derived under optimal conditions.