In this note, as an example, we introduoe a definition of general optimality in estimating a linear estimable function S<sub>k×p</sub> （S’ μ（X’）） of the mean matrix in multivariate linear mod...In this note, as an example, we introduoe a definition of general optimality in estimating a linear estimable function S<sub>k×p</sub> （S’ μ（X’）） of the mean matrix in multivariate linear model: Y<sub>n×m</sub>=X<sub>n×p</sub> +ε E（ε）=0, Cov（ ）=σ<sup>2</sup>U<sub>n×n</sub> V<sub>m×m</sub>, n≥m. In general, the general optimality of a parametric matrix follows analogously. The above X, S, U≥0 and V≥0 （but V≠0） are known matrix, and σ<sup>2</sup>】0 are unknown parameters, =（ε<sub>1</sub>’, ε<sub>2</sub>’, …, ε<sub>n</sub>’）’, where ε<sub>i</sub> is the ith row of ε, U V denotes the展开更多
In this paper a modified method for linear moment problem and the error estimate are presented. It is proven that the modified method is a kind of projection method under suitable conditions. Numericale examples are g...In this paper a modified method for linear moment problem and the error estimate are presented. It is proven that the modified method is a kind of projection method under suitable conditions. Numericale examples are given showing that this method is both accurate and simple to use.展开更多
The Rotary Inverted Pendulum(RIP)is a widely used underactuated mechanical system in various applications such as bipedal robots and skyscraper stabilization where attitude control presents a significant challenge.Des...The Rotary Inverted Pendulum(RIP)is a widely used underactuated mechanical system in various applications such as bipedal robots and skyscraper stabilization where attitude control presents a significant challenge.Despite the implementation of various control strategies to maintain equilibrium,optimally tuning control gains to effectively mitigate uncertain nonlinearities in system dynamics remains elusive.Existing methods frequently rely on extensive experimental data or the designer’s expertise,presenting a notable drawback.This paper proposes a novel tracking control approach for RIP,utilizing a Linear Quadratic Regulator(LQR)in combination with a reduced-order observer.Initially,the RIP system is mathematically modeled using the Newton-Euler-Lagrange method.Subsequently,a composite controller is devised that integrates an LQR for generating nominal control signals and a reduced-order observer for reconstructing unmeasured states.This approach enhances the controller’s robustness by eliminating differential terms from the observer,thereby attenuating unknown disturbances.Thorough numerical simulations and experimental evaluations demonstrate the system’s capability to maintain balance below50Hz and achieve precise tracking below1.4 rad,validating the effectiveness of the proposed control scheme.展开更多
For the functional partially linear models including flexible nonparametric part and functional linear part,the estimators of the nonlinear function and the slope function have been studied in existing literature.How ...For the functional partially linear models including flexible nonparametric part and functional linear part,the estimators of the nonlinear function and the slope function have been studied in existing literature.How to test the correlation between response and explanatory variables,however,still seems to be missing.Therefore,a test procedure for testing the linearity in the functional partially linear models will be proposed in this paper.A test statistic is constructed based on the existing estimators of the nonlinear and the slope functions.Further,we prove that the approximately asymptotic distribution of the proposed statistic is a chi-squared distribution under some regularity conditions.Finally,some simulation studies and a real data application are presented to demonstrate the performance of the proposed test statistic.展开更多
The authors establish the approximations to the distribution of M-estimates in a linear model by the bootstrap and the linear representation of bootstrap M-estimation, and prove that the approximation is valid in prob...The authors establish the approximations to the distribution of M-estimates in a linear model by the bootstrap and the linear representation of bootstrap M-estimation, and prove that the approximation is valid in probability 1. A simulation is made to show the effects of bootstrap approximation, randomly weighted approximation and normal approximation.展开更多
Consider the standard linear model where x_x,x_2… are assumed to be the known p-vectors, β the unknown p-vector of regression coefficients, and e_1, e_2, …the independent random error sequence, each having a median...Consider the standard linear model where x_x,x_2… are assumed to be the known p-vectors, β the unknown p-vector of regression coefficients, and e_1, e_2, …the independent random error sequence, each having a median zero. Define the minimum L_1norm estimator as,the solution of the minimization problem inf It is proved in this paper that is asymptotically normal under very weak conditions. In particular, the condition imposed on {xi} is exactly the same which ensures the asymptotic normality of least-squares estimate:展开更多
文摘In this note, as an example, we introduoe a definition of general optimality in estimating a linear estimable function S<sub>k×p</sub> （S’ μ（X’）） of the mean matrix in multivariate linear model: Y<sub>n×m</sub>=X<sub>n×p</sub> +ε E（ε）=0, Cov（ ）=σ<sup>2</sup>U<sub>n×n</sub> V<sub>m×m</sub>, n≥m. In general, the general optimality of a parametric matrix follows analogously. The above X, S, U≥0 and V≥0 （but V≠0） are known matrix, and σ<sup>2</sup>】0 are unknown parameters, =（ε<sub>1</sub>’, ε<sub>2</sub>’, …, ε<sub>n</sub>’）’, where ε<sub>i</sub> is the ith row of ε, U V denotes the
文摘In this paper a modified method for linear moment problem and the error estimate are presented. It is proven that the modified method is a kind of projection method under suitable conditions. Numericale examples are given showing that this method is both accurate and simple to use.
基金supported in part by the Youth Foundation of China University of Petroleum-Beijing at Karamay(under Grant No.XQZX20230038)the Karamay Innovative Talents Program(under Grant No.20212022HJCXRC0005).
文摘The Rotary Inverted Pendulum(RIP)is a widely used underactuated mechanical system in various applications such as bipedal robots and skyscraper stabilization where attitude control presents a significant challenge.Despite the implementation of various control strategies to maintain equilibrium,optimally tuning control gains to effectively mitigate uncertain nonlinearities in system dynamics remains elusive.Existing methods frequently rely on extensive experimental data or the designer’s expertise,presenting a notable drawback.This paper proposes a novel tracking control approach for RIP,utilizing a Linear Quadratic Regulator(LQR)in combination with a reduced-order observer.Initially,the RIP system is mathematically modeled using the Newton-Euler-Lagrange method.Subsequently,a composite controller is devised that integrates an LQR for generating nominal control signals and a reduced-order observer for reconstructing unmeasured states.This approach enhances the controller’s robustness by eliminating differential terms from the observer,thereby attenuating unknown disturbances.Thorough numerical simulations and experimental evaluations demonstrate the system’s capability to maintain balance below50Hz and achieve precise tracking below1.4 rad,validating the effectiveness of the proposed control scheme.
基金supported by the National Natural Science Foundation of China(No.12271370)。
文摘For the functional partially linear models including flexible nonparametric part and functional linear part,the estimators of the nonlinear function and the slope function have been studied in existing literature.How to test the correlation between response and explanatory variables,however,still seems to be missing.Therefore,a test procedure for testing the linearity in the functional partially linear models will be proposed in this paper.A test statistic is constructed based on the existing estimators of the nonlinear and the slope functions.Further,we prove that the approximately asymptotic distribution of the proposed statistic is a chi-squared distribution under some regularity conditions.Finally,some simulation studies and a real data application are presented to demonstrate the performance of the proposed test statistic.
基金supported by Fund of 211 Program of SHUFEFund of Educational Committee of Shanghai
文摘The authors establish the approximations to the distribution of M-estimates in a linear model by the bootstrap and the linear representation of bootstrap M-estimation, and prove that the approximation is valid in probability 1. A simulation is made to show the effects of bootstrap approximation, randomly weighted approximation and normal approximation.
基金Project supported by the National Natural Science Foundation of China and also supported by the U. S. Office of Naval Research and Air Force Office of Scientific Research.
文摘Consider the standard linear model where x_x,x_2… are assumed to be the known p-vectors, β the unknown p-vector of regression coefficients, and e_1, e_2, …the independent random error sequence, each having a median zero. Define the minimum L_1norm estimator as,the solution of the minimization problem inf It is proved in this paper that is asymptotically normal under very weak conditions. In particular, the condition imposed on {xi} is exactly the same which ensures the asymptotic normality of least-squares estimate:
