非线性系统基于降维状态观测器的反馈稳定化设计

本文研究了一类仿射非线性控制系统的反馈稳定化问题。     

一类二阶泛函微分方程振动解的性质

讨论了方程ｘ″（ｔ）＋ｐ（ｔ）ｆ（ｘ（ｇ（ｔ））＝ｒ（ｔ）振动解的渐近性和有界性，利用分离强迫项的方法，获得了几个新的结果．     

On the asymptotic stability of switched homogeneous systems

The stability of switched systems generated by the family of autonomous subsystems with homogeneous right-hand sides is investigated. It is assumed that for each subsystem the proper homogeneous Lyapunov function is constructed. The sufficient conditions of the existence of the common Lyapunov function providing global asymptotic stability of the zero solution for any admissible switching law are obtained. In the case where we can not guarantee the existence of a common Lyapunov function, the classes of switching signals are determined under which the zero solution is locally or globally asymptotically stable. It is proved that, for any given neighborhood of the origin, one can choose a number L>0 (dwell time) such that if intervals between consecutive switching times are not smaller than L then any solution of the considered system enters this neighborhood in finite time and remains within it thereafter.     

Asymptotic Stability and Finite‐Time Stability of Networked Control Systems: Analysis and Synthesis

This paper focuses on the problems of asymptotic stability and finite‐time stability (FTS) analysis, along with the state feedback controller design for networked control systems (NCSs) with consideration of both network‐induced delay and packet dropout. The closed‐loop NCS is modeled as a discrete‐time linear system with a time‐varying, bounded state delay. Sufficient conditions for the asymptotic stability and the FTS of the closed‐loop NCS are provided, respectively. Based on the stability analysis results, a mixed controller design method, which guarantees the asymptotic stability of the closed‐loop NCS in the usual case and the FTS of the closed‐loop NCS in the unusual case (that is, in some particular time intervals, large state delay occurs), is presented. A numerical example is provided to illustrate the effectiveness of the proposed mixed controller design method.     

On the accuracy in errors-in-variables identification compared to prediction-error identification

Errors-in-variables estimation problems for single-input–single-output systems with Gaussian signals are considered in this contribution. It is shown that the Fisher information matrix is monotonically increasing as a function of the input noise variance when the noise spectrum at the input is known and the corresponding noise variance is estimated. Furthermore, it is shown that Whittle’s formula for the Fisher information matrix can be represented as a Gramian and this is used to provide a geometric representation of the asymptotic covariance matrix for asymptotically efficient estimators. Finally, the asymptotic covariance of the parameter estimates for the system dynamics is compared for the two cases: (i) when the model includes white measurement noise on the input and the variance of the noise is estimated, and (ii) when the model includes only measurement noise on the output. In both cases, asymptotically efficient estimators are assumed. An explicit expression for the difference is derived when the underlying system is subject only to measurement noise on the output.     

Asymptotic boundary conditions with immersed finite elements for interface magnetostatic/electrostatic field problems with open boundary

Many of the magnetostatic/electrostatic field problems encountered in aerospace engineering, such as plasma sheath simulation and ion neutralization process in space, are not confined to finite domain and non-interface problems, but characterized as open boundary and interface problems. Asymptotic boundary conditions (ABC) and immersed finite elements (IFE) are relatively new tools to handle open boundaries and interface problems respectively. Compared with the traditional truncation approach, asymptotic boundary conditions need a much smaller domain to achieve the same accuracy. When regular finite element methods are applied to an interface problem, it is necessary to use a body-fitting mesh in order to obtain the optimal convergence rate. However, immersed finite elements possess the same optimal convergence rate on a Cartesian mesh, which is critical to many applications. This paper applies immersed finite element methods and asymptotic boundary conditions to solve an interface problem arising from electric field simulation in composite materials with open boundary. Numerical examples are provided to demonstrate the high global accuracy of the IFE method with ABC based on Cartesian meshes, especially around both interface and boundary. This algorithm uses a much smaller domain than the truncation approach in order to achieve the same accuracy.     

Inferences on Weibull parameters with conventional type-I censoring

In this article we consider the statistical inferences of the unknown parameters of a Weibull distribution when the data are Type-I censored. It is well known that the maximum likelihood estimators do not always exist, and even when they exist, they do not have explicit expressions. We propose a simple fixed point type algorithm to compute the maximum likelihood estimators, when they exist. We also propose approximate maximum likelihood estimators of the unknown parameters, which have explicit forms. We construct the confidence intervals of the unknown parameters using asymptotic distribution and also by using the bootstrapping technique. Bayes estimates and the corresponding highest posterior density credible intervals of the unknown parameters are also obtained under fairly general priors on the unknown parameters. The Bayes estimates cannot be obtained explicitly. We propose to use the Gibbs sampling technique to compute the Bayes estimates and also to construct the highest posterior density credible intervals. Different methods have been compared by Monte Carlo simulations. One real data set has been analyzed for illustrative purposes.     

Partially varying coefficient single index proportional hazards regression models

In this paper, the partially varying coefficient single index proportional hazards regression models are discussed. All unknown functions are fitted by polynomial B splines. The index parameters and B-spline coefficients are estimated by the partial likelihood method and a two-step Newton-Raphson algorithm. Consistency and asymptotic normality of the estimators of all the parameters are derived. Through a simulation study and the VA data example, we illustrate that the proposed estimation procedure is accurate, rapid and stable.     

Asymptotic behavior of positive solutions of sublinear differential equations of Emden-Fowler type

This paper is concerned with asymptotic analysis of positive solutions of the second-order nonlinear differential equation

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