Parameter Estimation of Time-Varying ARMA Model

The auto-regressive moving-average (ARMA) model with time-varying parameters is analyzed. The time-varying parameters are assumed to be a linear combination of a set of basis time-varying functions, and the feedback linear estimation algorithm is used to estimate the time-varying parameters of the ARMA model. This algorithm includes 2 linear least squares estimations and a linear filter. The influence of the order of basis time-(varying) functions on parameters estimation is analyzed. The method has the advantage of simple, saving computation time and storage space. Theoretical analysis and experimental results show the validity of this method.

STRONG CONVERGENCE RATES OF SEVERAL ESTIMATORS IN SEMIPARAMETRIC VARYING-COEFFICIENT PARTIALLY LINEAR MODELS

This article is concerned with the estimating problem of semiparametric varyingcoefficient partially linear regression models. By combining the local polynomial and least squares procedures Fan and Huang （2005） proposed a profile least squares estimator for the parametric component and established its asymptotic normality. We further show that the profile least squares estimator can achieve the law of iterated logarithm. Moreover, we study the estimators of the functions characterizing the non-linear part as well as the error variance. The strong convergence rate and the law of iterated logarithm are derived for them, respectively.

Efficient Shrinkage Estimation about the Partially Linear Varying Coefficient Model with Random Effect for Longitudinal Data

In this paper, an efficient shrinkage estimation procedure for the partially linear varying coefficient model (PLVC) with random effect is considered. By selecting the significant variable and estimating the nonzero coefficient, the model structure specification is accomplished by introducing a novel penalized estimating equation. Under some mild conditions, the asymptotic properties for the proposed model selection and estimation results, such as the sparsity and oracle property, are established. Some numerical simulation studies and a real data analysis are presented to examine the finite sample performance of the procedure.

A Survey of Output Feedback Robust MPC for Linear Parameter Varying Systems

For constrained linear parameter varying(LPV)systems,this survey comprehensively reviews the literatures on output feedback robust model predictive control(OFRMPC)over the past two decades from the aspects on motivations,main contributions,and the related techniques.According to the types of state observer systems and scheduling parameters of LPV systems,different kinds of OFRMPC approaches are summarized and compared.The extensions of OFRMPC for LPV systems to other related uncertain systems are also investigated.The methods of dealing with system uncertainties and constraints in different kinds of OFRMPC optimizations are given.Key issues on OFRMPC optimizations for LPV systems are discussed.Furthermore,the future research directions on OFRMPC for LPV systems are suggested.

Generalized Likelihood Ratio Tests for Varying-Coefficient Models with Censored Data

In this paper, we extend the generalized likelihood ratio test to the varying-coefficient models with censored data. We investigate the asymptotic behavior of the proposed test and demonstrate that its limiting null distribution follows a distribution, with the scale constant and the number of degree of freedom being independent of nuisance parameters or functions, which is called the wilks phenomenon. Both simulated and real data examples are given to illustrate the performance of the testing approach.

TESTING SERIAL CORRELATION IN SEMIPARAMETRIC VARYING COEFFICIENT PARTIALLY LINEAR ERRORS-IN-VARIABLES MODEL

The authors propose a V_(N,p) test statistic for testing finite-order serial correlation in asemiparametric varying coefficient partially linear errors-in-variables model.The test statistic is shownto have asymptotic normal distribution under the null hypothesis of no serial correlation.Some MonteCarlo experiments are conducted to examine the finite sample performance of the proposed V_(N,p) teststatistic.Simulation results confirm that the proposed test performs satisfactorily in estimated sizeand power.

Variable Selection for Generalized Varying Coefficient Partially Linear Models with Diverging Number of Parameters

Semiparametric models with diverging number of predictors arise in many contemporary scientific areas. Variable selection for these models consists of two components： model selection for non-parametric components and selection of significant variables for the parametric portion. In this paper, we consider a variable selection procedure by combining basis function approximation with SCAD penalty. The proposed procedure simultaneously selects significant variables in the parametric components and the nonparametric components. With appropriate selection of tuning parameters, we establish the consistency and sparseness of this procedure.

Penalized profile least squares-based statistical inference for varying coefficient partially linear errors-in-variables models

The purpose of this paper is two fold. First, we investigate estimation for varying coefficient partially linear models in which covariates in the nonparametric part are measured with errors. As there would be some spurious covariates in the linear part, a penalized profile least squares estimation is suggested with the assistance from smoothly clipped absolute deviation penalty. However, the estimator is often biased due to the existence of measurement errors, a bias correction is proposed such that the estimation consistency with the oracle property is proved. Second, based on the estimator, a test statistic is constructed to check a linear hypothesis of the parameters and its asymptotic properties are studied. We prove that the existence of measurement errors causes intractability of the limiting null distribution that requires a Monte Carlo approximation and the absence of the errors can lead to a chi-square limit. Furthermore, confidence regions of the parameter of interest can also be constructed. Simulation studies and a real data example are conducted to examine the performance of our estimators and test statistic.

LVP Modeling and Dynamic Characteristics Prediction of A Hydraulic Power Unit in Deep-Sea

A hydraulic power unit （HPU） is the driving ＂heart＂ of deep-sea working equipment. It is critical to predict its dynamic performances in deep-water before being immerged in the seawater, while the experimental tests by simulating deep-sea environment have many disadvantages, such as expensive cost, long test cycles, and difficult to achieve low-temperature simulation, which is only used as a supplementary means for confirmatory experiment. This paper proposes a novel theoretical approach based on the linear varying parameters （LVP） modeling to foresee the dynamic performances of the driving unit. Firstly, based on the varying environment features, dynamic expressions of the compressibility and viscosity of hydranlic oil are derived to reveal the fluid performances changing. Secondly, models of hydraulic system and electrical system are accomplished respectively through studying the control process and energy transfer, and then LVP models of the pressure and flow rate control is obtained through the electro-hydraulic models integration. Thirdly, dynamic characteristics of HPU are obtained by the model simulating within bounded closed sets of varying parameters. Finally, the developed HPU is tested in a deep-sea imitating hull, and the experimental results are well consistent with the theoretical analysis outcomes, which clearly declare that the LVP modeling is a rational way to foresee dynamic performances of HPU. The research approach and model analysis results can be applied to the predictions of working properties and product designs for other deep-sea hydraulic pump.

HOSVD-based LPV modeling and mixed robust H_2/H_∞ control design for air-breathing hypersonic vehicle

This paper focuses on synthesizing a mixed robust H_2/H_∞ linear parameter varying（LPV） controller for the longitudinal motion of an air-breathing hypersonic vehicle via a high order singular value decomposition（HOSVD） approach.The design of hypersonic flight control systems is highly challenging due to the enormous complexity of the vehicle dynamics and the presence of significant uncertainties.Motivated by recent results on both LPV control and tensor-product（TP） model transformation approach,the velocity and altitude tracking control problems for the air-breathing hypersonic vehicle is reduced to that of a state feedback stabilizing controller design for a polytopic LPV system with guaranteed performances.The controller implementation is converted into a convex optimization problem with parameterdependent linear matrix inequalities（LMIs） constraints,which is intuitively tractable using LMI control toolbox.Finally,numerical simulation results demonstrate the effectiveness of the proposed approach.

Variable Selection for Semiparametric Varying-Coefficient Partially Linear Models with Missing Response at Random

In this paper, we present a variable selection procedure by combining basis function approximations with penalized estimating equations for semiparametric varying-coefficient partially linear models with missing response at random. The proposed procedure simultaneously selects significant variables in parametric components and nonparametric components. With appropriate selection of the tuning parameters, we establish the consistency of the variable selection procedure and the convergence rate of the regularized estimators. A simulation study is undertaken to assess the finite sample performance of the proposed variable selection procedure.

A High-order Internal Model Based Iterative Learning Control Scheme for Discrete Linear Time-varying Systems

In this paper, an iterative learning control algorithm is proposed for discrete linear time-varying systems to track iterationvarying desired trajectories. A high-order internal model(HOIM) is utilized to describe the variation of desired trajectories in the iteration domain. In the sequel, the HOIM is incorporated into the design of learning gains. The learning convergence in the iteration axis can be guaranteed with rigorous proof. The simulation results with permanent magnet linear motors(PMLM) demonstrate that the proposed HOIM based approach yields good performance and achieves perfect tracking.

Partially Time-varying Coefficient Linear Rate Model for the Recurrent Event Data

In [13], Schaubel et al. proposed a semiparametric partially linear rate model for the statistical analysis of recurrent event data. But they only considered the model with time-independent covariate effects. In this paper, rate function of the recurrent event is modeled by a semipaxametric partially linear function which can include the time-varying effects. We propose the method of generalized estimating equations to make inferences about both the time-varying effects and time-independent effects. The large sample properties are established, while extensive simulation studies are carried out to examine the proposed procedures. At last, we apply the procedures to the well-known bladder cancer study.

Shrinkage Estimation of Semiparametric Model with Missing Responses for Cluster Data

This paper simultaneously investigates variable selection and imputation estimation of semiparametric partially linear varying-coefficient model in that case where there exist missing responses for cluster data. As is well known, commonly used approach to deal with missing data is complete-case data. Combined the idea of complete-case data with a discussion of shrinkage estimation is made on different cluster. In order to avoid the biased results as well as improve the estimation efficiency, this article introduces Group Least Absolute Shrinkage and Selection Operator (Group Lasso) to semiparametric model. That is to say, the method combines the approach of local polynomial smoothing and the Least Absolute Shrinkage and Selection Operator. In that case, it can conduct nonparametric estimation and variable selection in a computationally efficient manner. According to the same criterion, the parametric estimators are also obtained. Additionally, for each cluster, the nonparametric and parametric estimators are derived, and then compute the weighted average per cluster as finally estimators. Moreover, the large sample properties of estimators are also derived respectively.

变长分段直线感应电机数学建模

变长分段直线感应电机参数具有不连续、快速时变及强耦合特性,这给电磁暂态建模带来挑战。该文引入3种时变因子推导出具有参数时变特性的变长分段直线感应电机数学表达式。通过分析变长分段直线感应电机定子与动子的电磁耦合特性及时变因子与状态变量之间的耦合关系,建立定子、动子及时变因子相互解耦的数学模型。仿真结果表明,该数学模型计算的电压、电流和速度与有限元计算结果差别小于6%,验证了数学模型的准确性。硬件在环实验结果表明,在高速工况下数学模型可以准确模拟系统的电磁暂态特性,验证了数学模型的解耦能力及数值运算稳定性。

基于辅助回归的面板数据固定效应变系数模型的估计

本文针对面板数据固定效应变系数模型引入辅助回归来解释个体效应与协变量之间的关系,以此来处理固定效应,将模型转化为部分线性变系数模型.为了获得系数函数的估计,采用正交投影的方法消除固定效应,进一步基于局部线性估计对系数函数进行估计.在一些正则条件下,给出了系数函数估计的渐近性质.随后,模拟研究了所提出的估计方法的有限样本性质.模拟结果表明无论个体效应是随机的还是固定的,本文方法优于已有的方法.最后,对艾滋病人的CD4数据进行了实证分析.

部分线性变系数空间自回归模型的惩罚轮廓拟最大似然方法

主要研究了部分线性变系数空间自回归模型的变量选择问题。结合拟最大似然方法、局部线性光滑方法以及一类非凸罚函数,提出了一个变量选择方法用于同时选择该模型的参数部分中重要解释变量和估计相应的非零参数。大量模拟研究表明,所提出的变量选择方法具有满意的有限样本性质,并且关于空间权矩阵的稀疏度、空间相关强度、系数函数的复杂度以及误差分布的非正态性非常稳健。特别地,当样本容量较大且罚函数选择合适时,即使解释变量的相关性较强或者模型中含有较多不重要解释变量,所提出的变量选择方法仍然具有比较满意的有限样本性质。通过分析波士顿房屋价格数据考察了所提出的变量选择方法的实际应用效果。

空间堆线性变参数模型预测控制方法

针对传统PID控制方法在面临复杂负荷需求变化时无法满足空间核反应堆的控制性能需求的问题,提出了基于线性变参数模型的空间堆模型预测控制方法。针对强非线性特性,采用线性变参数模型作为预测模型,对全功率范围内的空间堆运行特性进行预测;针对大时滞的特性,采用串级控制理论结合模型预测方法优化执行机构动作,提升被控量的响应速度。分别设计了电功率和冷却剂温度的预测控制系统,在典型工况下进行控制性能仿真验证,结果表明:相对于串级PID控制系统,所设计的预测控制系统的电功率调节时间减少了68.7%,冷却剂温度调节时间减少了81.7%;电功率和冷却剂温度预测控制系统的核功率的超调量分别减少了22.3%和13.0%,保证了反应堆的安全;控制系统的适用性强,在不同功率水平均具有良好的控制性能;执行机构的动作大幅减少,驱动电机峰值电压下降了84.1%,使用寿命得到延长,系统经济性得到提升。该研究提出的结合串级控制理论基于线性变参数模型的预测控制方法能够用于优化空间堆的控制系统。

基于LPV-MPC的风电机组功率-载荷协调控制策略

大型风电机组变桨控制是一个复杂的非线性控制任务,如何在系统约束和风速扰动的条件下实现功率调节和载荷降低成为难题。针对该问题,文章采用机理与参数辨识方法构建了一个面向控制的线性变参数(LPV)模型,LPV模型引入间隙度量理论来降低模型复杂度,为控制设计提供了更加精确的线性模型。设计了时变卡尔曼滤波器,实现了风机的最优状态估计,基于获得的最优状态,提出了自适应模型预测(MPC)变桨控制器,MPC控制器能够根据实时风速变化调整预测模型,在满足系统约束的条件下实现大型风电机组功率-载荷的协调控制。OpenFAST对比仿真实例表明了模型与控制器的有效性。