The unique Bayes linear unbiased estimator (Bayes LUE) of estimable functions is derived for the singular linear model. The superiority of Bayes LUE over ordinary best linear unbiased estimator is investigated under m...The unique Bayes linear unbiased estimator (Bayes LUE) of estimable functions is derived for the singular linear model. The superiority of Bayes LUE over ordinary best linear unbiased estimator is investigated under mean square error matrix (MSEM)criterion.展开更多
Consider the partitioned linear regression model and its four reduced linear models, where y is an n × 1 observable random vector with E(y) = Xβ and dispersion matrix Var(y) = σ2 V, where σ2 is an unknown pos...Consider the partitioned linear regression model and its four reduced linear models, where y is an n × 1 observable random vector with E(y) = Xβ and dispersion matrix Var(y) = σ2 V, where σ2 is an unknown positive scalar, V is an n × n known symmetric nonnegative definite matrix, X = (X 1 : X 2) is an n×(p+q) known design matrix with rank(X) = r ≤ (p+q), and β = (β′ 1: β′2 )′ with β1 and β2 being p×1 and q×1 vectors of unknown parameters, respectively. In this article the formulae for the differences between the best linear unbiased estimators of M 2 X 1β1under the model and its best linear unbiased estimators under the reduced linear models of are given, where M 2 = I -X 2 X 2 + . Furthermore, the necessary and sufficient conditions for the equalities between the best linear unbiased estimators of M 2 X 1β1 under the model and those under its reduced linear models are established. Lastly, we also study the connections between the model and its linear transformation model.展开更多
For a singular linear model A = （y, Xβ, σ2 V） and its transformed model MF = （Fy, FXβ, σ 2FVF＇）, where V is nonnegative definite and X can be rank-deficient, the expressions for the differences of the estimat...For a singular linear model A = （y, Xβ, σ2 V） and its transformed model MF = （Fy, FXβ, σ 2FVF＇）, where V is nonnegative definite and X can be rank-deficient, the expressions for the differences of the estimates for the vector of FXβ and the variance factor σ2 are given. Moreover, the necessary and sufficient conditions for the equalities of the estimates for the vector of FXβ and the variance factor σ2 are also established. In the meantime, works in Baksalary and Kala （1981） are strengthened and consequences in Puntanen and Nurhonen （1992）, and Puntanen （1996） are extended.展开更多
By using the hypothesis of the deformation of the straight bar and beam in mechanics of materials,a new engineering calculating model for a linear inclusion in plane is presented.Through the Kelvin's solution of a...By using the hypothesis of the deformation of the straight bar and beam in mechanics of materials,a new engineering calculating model for a linear inclusion in plane is presented.Through the Kelvin's solution of a concentrated force,the inclusion problem is reduced to solving a set of uncoupled singular integral equations which can be solved by the numerical method of singular integral equation.Based on these results,several applicable examples including an inclusion-crack problem are calculated and the results are quite satisfactory.展开更多
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（H...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.展开更多
基金This work was supported by the Doctoral Program Foundation of the Institute of High Educationthe Special Foundation of Chinese Academy of Sciences.
文摘The unique Bayes linear unbiased estimator (Bayes LUE) of estimable functions is derived for the singular linear model. The superiority of Bayes LUE over ordinary best linear unbiased estimator is investigated under mean square error matrix (MSEM)criterion.
基金supported by the National Natural Science Foundation of ChinaTian Yuan Special Foundation (No.10226024)Postdoctoral Foundation of China and Lab.of Math.for Nonlinear Sciences at Fudan Universitysupported in part by The International Organizing Committee and The Local Organizing Committee at the University of Tampere for this Workshopsupported in part by an NSF grant of China
文摘Consider the partitioned linear regression model and its four reduced linear models, where y is an n × 1 observable random vector with E(y) = Xβ and dispersion matrix Var(y) = σ2 V, where σ2 is an unknown positive scalar, V is an n × n known symmetric nonnegative definite matrix, X = (X 1 : X 2) is an n×(p+q) known design matrix with rank(X) = r ≤ (p+q), and β = (β′ 1: β′2 )′ with β1 and β2 being p×1 and q×1 vectors of unknown parameters, respectively. In this article the formulae for the differences between the best linear unbiased estimators of M 2 X 1β1under the model and its best linear unbiased estimators under the reduced linear models of are given, where M 2 = I -X 2 X 2 + . Furthermore, the necessary and sufficient conditions for the equalities between the best linear unbiased estimators of M 2 X 1β1 under the model and those under its reduced linear models are established. Lastly, we also study the connections between the model and its linear transformation model.
基金The project was supported by the Mathematical Tian Yuan Youth Foundation of China (10226024)Postdoctoral Science Foundation of Chinathe Science Foundation for Yong Teachers of Northeast Normal University.
文摘For a singular linear model A = （y, Xβ, σ2 V） and its transformed model MF = （Fy, FXβ, σ 2FVF＇）, where V is nonnegative definite and X can be rank-deficient, the expressions for the differences of the estimates for the vector of FXβ and the variance factor σ2 are given. Moreover, the necessary and sufficient conditions for the equalities of the estimates for the vector of FXβ and the variance factor σ2 are also established. In the meantime, works in Baksalary and Kala （1981） are strengthened and consequences in Puntanen and Nurhonen （1992）, and Puntanen （1996） are extended.
基金The project supported by National Natural Science Foundation of China.
文摘By using the hypothesis of the deformation of the straight bar and beam in mechanics of materials,a new engineering calculating model for a linear inclusion in plane is presented.Through the Kelvin's solution of a concentrated force,the inclusion problem is reduced to solving a set of uncoupled singular integral equations which can be solved by the numerical method of singular integral equation.Based on these results,several applicable examples including an inclusion-crack problem are calculated and the results are quite satisfactory.
基金supported by the National Natural Science Foundation of China(6120300761304239+1 种基金61503392)the Natural Science Foundation of Shaanxi Province(2015JQ6213)
文摘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.
