This paper focuses on boundary stabilization of a one-dimensional wave equation with an unstable boundary condition,in which observations are subject to arbitrary fixed time delay.The observability inequality indicate...This paper focuses on boundary stabilization of a one-dimensional wave equation with an unstable boundary condition,in which observations are subject to arbitrary fixed time delay.The observability inequality indicates that the open-loop system is observable,based on which the observer and predictor are designed:The state of system is estimated with available observation and then predicted without observation.After that equivalently the authors transform the original system to the well-posed and exponentially stable system by backstepping method.The equivalent system together with the design of observer and predictor give the estimated output feedback.It is shown that the closed-loop system is exponentially stable.Numerical simulations are presented to illustrate the effect of the stabilizing controller.展开更多
Longitudinal data often occur in follow-up studies, and in many situations, there may exist informative observation times and a dependent terminal event such as death that stops the follow-up. We propose a semiparamet...Longitudinal data often occur in follow-up studies, and in many situations, there may exist informative observation times and a dependent terminal event such as death that stops the follow-up. We propose a semiparametric mixed effect model with time-varying latent effects in the analysis of longitudinal data with informative observation times and a dependent terminal event. Estimating equation approaches are developed for parameter estimation, and asymptotic properties of the resulting estimators are established. The finite sample behavior of the proposed estimators is evaluated through simulation studies, and an application to a bladder cancer study is provided.展开更多
基金supported by the National Natural Science Foundation of China under Grant No.61203058the Training Program for Outstanding Young Teachers of North China University of Technology under Grant No.XN131+1 种基金the Construction Plan for Innovative Research Team of North China University of Technology under Grant No.XN129the Laboratory construction for Mathematics Network Teaching Platform of North China University of Technology under Grant No.XN041
文摘This paper focuses on boundary stabilization of a one-dimensional wave equation with an unstable boundary condition,in which observations are subject to arbitrary fixed time delay.The observability inequality indicates that the open-loop system is observable,based on which the observer and predictor are designed:The state of system is estimated with available observation and then predicted without observation.After that equivalently the authors transform the original system to the well-posed and exponentially stable system by backstepping method.The equivalent system together with the design of observer and predictor give the estimated output feedback.It is shown that the closed-loop system is exponentially stable.Numerical simulations are presented to illustrate the effect of the stabilizing controller.
基金supported by National Natural Science Foundation of China (Grant Nos. 11231010, 11171330 and 11201315)Key Laboratory of Random Complex Structures and Data Science, Chinese Academy of Sciences (Grant No. 2008DP173182)Beijing Center for Mathematics and Information Interdisciplinary Sciences
文摘Longitudinal data often occur in follow-up studies, and in many situations, there may exist informative observation times and a dependent terminal event such as death that stops the follow-up. We propose a semiparametric mixed effect model with time-varying latent effects in the analysis of longitudinal data with informative observation times and a dependent terminal event. Estimating equation approaches are developed for parameter estimation, and asymptotic properties of the resulting estimators are established. The finite sample behavior of the proposed estimators is evaluated through simulation studies, and an application to a bladder cancer study is provided.
