This paper studies the parameter estimation problems of the nonlinear systems described by the bilinear state space models in the presence of disturbances.A bilinear state observer is designed for deriving identificat...This paper studies the parameter estimation problems of the nonlinear systems described by the bilinear state space models in the presence of disturbances.A bilinear state observer is designed for deriving identification algorithms to estimate the state variables using the input-output data.Based on the bilinear state observer,a novel gradient iterative algorithm is derived for estimating the parameters of the bilinear systems by means of the continuous mixed p-norm cost function.The gain at each iterative step adapts to the data quality so that the algorithm has good robustness to the noise disturbance.Furthermore,to improve the performance of the proposed algorithm,a dynamicmoving window is designed which can update the dynamical data by removing the oldest data and adding the newestmeasurement data.A numerical example of identification of bilinear systems is presented to validate the theoretical analysis.展开更多
A number of previous papers have studied the problem of recovering low-rank matrices with noise, further combining the noisy and perturbed cases, we propose a nonconvex Schatten p-norm minimization method to deal with...A number of previous papers have studied the problem of recovering low-rank matrices with noise, further combining the noisy and perturbed cases, we propose a nonconvex Schatten p-norm minimization method to deal with the recovery of fully perturbed low-rank matrices. By utilizing the p-null space property (p-NSP) and the p-restricted isometry property (p-RIP) of the matrix, sufficient conditions to ensure that the stable and accurate reconstruction for low-rank matrix in the case of full perturbation are derived, and two upper bound recovery error estimation ns are given. These estimations are characterized by two vital aspects, one involving the best r-approximation error and the other concerning the overall noise. Specifically, this paper obtains two new error upper bounds based on the fact that p-RIP and p-NSP are able to recover accurately and stably low-rank matrix, and to some extent improve the conditions corresponding to RIP.展开更多
For a convex set-valued map between p-normed (0 < p < 1) spaces, we give a criterion for its inverse to be locally Lipschitz of order p. From this we obtain the Robinson-Ursescu Theorem in p-normed spaces and th...For a convex set-valued map between p-normed (0 < p < 1) spaces, we give a criterion for its inverse to be locally Lipschitz of order p. From this we obtain the Robinson-Ursescu Theorem in p-normed spaces and the open mapping and closed graph theorems for closed convex set-valued maps.展开更多
在信号处理领域,传统的自适应滤波算法采用的固定步长会导致稳态误差和收敛速度无法同时兼顾。针对这个问题,对最小平均p范数(Least Mean p-norm,LMP)算法进行改进,提出了一种基于改进双曲正切(tanh)函数的变步长最小平均p范数算法。该...在信号处理领域,传统的自适应滤波算法采用的固定步长会导致稳态误差和收敛速度无法同时兼顾。针对这个问题,对最小平均p范数(Least Mean p-norm,LMP)算法进行改进,提出了一种基于改进双曲正切(tanh)函数的变步长最小平均p范数算法。该算法利用改进的tanh函数来调节步长,采用移动加权平均法构造变步长函数;同时引入了一个调节函数以进一步提升算法的性能。通过在海洋脉冲噪声干扰下进行仿真,实验表明,与已有的固定步长和变步长算法相比,改进的变步长LMP算法较好地兼顾系统的收敛速度和稳态误差;引入调节函数后的新算法在保证原有算法收敛速度的同时进一步降低了算法的稳态误差,从而兼顾了算法的收敛性和稳定性,具有较好的可行性。展开更多
In this paper,we investigate some properties of dual complex numbers,dual complex vectors,and dual complex matrices.First,based on the magnitude of the dual complex number,we study the Young inequality,the Hölder...In this paper,we investigate some properties of dual complex numbers,dual complex vectors,and dual complex matrices.First,based on the magnitude of the dual complex number,we study the Young inequality,the Hölder inequality,and the Minkowski inequality in the setting of dual complex numbers.Second,we define the p-norm of a dual complex vector,which is a nonnegative dual number,and show some related properties.Third,we study the properties of eigenvalues of unitary matrices and unitary triangulation of arbitrary dual complex matrices.In particular,we introduce the operator norm of dual complex matrices induced by the p-norm of dual complex vectors,and give expressions of three important operator norms of dual complex matrices.展开更多
针对α稳定分布噪声环境下的自适应滤波问题,提出一种新的基于梯度范数的变步长归一化最小平均p范数(variable step-size normalized least mean p-norm,VSS-NLMP)算法。该算法首先对梯度矢量进行加权平滑,以减小梯度噪声的影响,然后利...针对α稳定分布噪声环境下的自适应滤波问题,提出一种新的基于梯度范数的变步长归一化最小平均p范数(variable step-size normalized least mean p-norm,VSS-NLMP)算法。该算法首先对梯度矢量进行加权平滑,以减小梯度噪声的影响,然后利用梯度矢量能够跟踪自适应过程的均方偏差这一特点,利用梯度矢量的欧氏范数控制步长的变化。给出了新算法的迭代过程,然后对其收敛性进行分析,仿真结果表明本算法较现有变步长NLMP算法有更好的性能。展开更多
在强脉冲噪声干扰背景中,核递归最小二乘(Kernel Recursive Least Square,KRLS)算法和核递归最大相关熵(Kernel Recursive Maximum Correntropy,KRMC)算法对非线性信号预测性能严重退化,对此提出一种核递归最小平均P范数(Kernel Recursi...在强脉冲噪声干扰背景中,核递归最小二乘(Kernel Recursive Least Square,KRLS)算法和核递归最大相关熵(Kernel Recursive Maximum Correntropy,KRMC)算法对非线性信号预测性能严重退化,对此提出一种核递归最小平均P范数(Kernel Recursive Least Mean P-norm,KRLMP)算法。首先运用核方法将输入数据映射到再生核希尔伯特空间(Reproducing Kernnel Hilbert Space,RKHS)。其次基于最小P范数准则和正则化方法,推导得到自适应滤波器的最佳权向量,其降低了非高斯脉冲和样本量少的影响。然后利用矩阵求逆理论,推导得到矩阵的递归公式。最后利用核技巧得到在输入空间高效计算的滤波器输出和算法的迭代公式。α稳定分布噪声背景下Mackey-Glass时间序列预测的仿真结果表明:KRLMP算法与KRLS算法和KRMC算法相比,抗脉冲噪声能力强,鲁棒性好。展开更多
Few study gives guidance to design weighting filters according to the frequency weighting factors,and the additional evaluation method of automotive ride comfort is not made good use of in some countries.Based on the ...Few study gives guidance to design weighting filters according to the frequency weighting factors,and the additional evaluation method of automotive ride comfort is not made good use of in some countries.Based on the regularities of the weighting factors,a method is proposed and the vertical and horizontal weighting filters are developed.The whole frequency range is divided several times into two parts with respective regularity.For each division,a parallel filter constituted by a low-and a high-pass filter with the same cutoff frequency and the quality factor is utilized to achieve section factors.The cascading of these parallel filters obtains entire factors.These filters own a high order.But,low order filters are preferred in some applications.The bilinear transformation method and the least P-norm optimal infinite impulse response（IIR） filter design method are employed to develop low order filters to approximate the weightings in the standard.In addition,with the window method,the linear phase finite impulse response（FIR） filter is designed to keep the signal from distorting and to obtain the staircase weighting.For the same case,the traditional method produces 0.330 7 m · s^–2 weighted root mean square（r.m.s.） acceleration and the filtering method gives 0.311 9 m · s^–2 r.m.s.The fourth order filter for approximation of vertical weighting obtains 0.313 9 m · s^–2 r.m.s.Crest factors of the acceleration signal weighted by the weighting filter and the fourth order filter are 3.002 7 and 3.011 1,respectively.This paper proposes several methods to design frequency weighting filters for automotive ride comfort evaluation,and these developed weighting filters are effective.展开更多
基金funded by the National Natural Science Foundation of China(No.61773182)the 111 Project(B12018).
文摘This paper studies the parameter estimation problems of the nonlinear systems described by the bilinear state space models in the presence of disturbances.A bilinear state observer is designed for deriving identification algorithms to estimate the state variables using the input-output data.Based on the bilinear state observer,a novel gradient iterative algorithm is derived for estimating the parameters of the bilinear systems by means of the continuous mixed p-norm cost function.The gain at each iterative step adapts to the data quality so that the algorithm has good robustness to the noise disturbance.Furthermore,to improve the performance of the proposed algorithm,a dynamicmoving window is designed which can update the dynamical data by removing the oldest data and adding the newestmeasurement data.A numerical example of identification of bilinear systems is presented to validate the theoretical analysis.
文摘A number of previous papers have studied the problem of recovering low-rank matrices with noise, further combining the noisy and perturbed cases, we propose a nonconvex Schatten p-norm minimization method to deal with the recovery of fully perturbed low-rank matrices. By utilizing the p-null space property (p-NSP) and the p-restricted isometry property (p-RIP) of the matrix, sufficient conditions to ensure that the stable and accurate reconstruction for low-rank matrix in the case of full perturbation are derived, and two upper bound recovery error estimation ns are given. These estimations are characterized by two vital aspects, one involving the best r-approximation error and the other concerning the overall noise. Specifically, this paper obtains two new error upper bounds based on the fact that p-RIP and p-NSP are able to recover accurately and stably low-rank matrix, and to some extent improve the conditions corresponding to RIP.
基金The NSF (Q1107107) of Jiangsu Educational Commission.
文摘For a convex set-valued map between p-normed (0 < p < 1) spaces, we give a criterion for its inverse to be locally Lipschitz of order p. From this we obtain the Robinson-Ursescu Theorem in p-normed spaces and the open mapping and closed graph theorems for closed convex set-valued maps.
文摘在信号处理领域,传统的自适应滤波算法采用的固定步长会导致稳态误差和收敛速度无法同时兼顾。针对这个问题,对最小平均p范数(Least Mean p-norm,LMP)算法进行改进,提出了一种基于改进双曲正切(tanh)函数的变步长最小平均p范数算法。该算法利用改进的tanh函数来调节步长,采用移动加权平均法构造变步长函数;同时引入了一个调节函数以进一步提升算法的性能。通过在海洋脉冲噪声干扰下进行仿真,实验表明,与已有的固定步长和变步长算法相比,改进的变步长LMP算法较好地兼顾系统的收敛速度和稳态误差;引入调节函数后的新算法在保证原有算法收敛速度的同时进一步降低了算法的稳态误差,从而兼顾了算法的收敛性和稳定性,具有较好的可行性。
基金the National Natural Science Foundation of China(Grant No.11871051).
文摘In this paper,we investigate some properties of dual complex numbers,dual complex vectors,and dual complex matrices.First,based on the magnitude of the dual complex number,we study the Young inequality,the Hölder inequality,and the Minkowski inequality in the setting of dual complex numbers.Second,we define the p-norm of a dual complex vector,which is a nonnegative dual number,and show some related properties.Third,we study the properties of eigenvalues of unitary matrices and unitary triangulation of arbitrary dual complex matrices.In particular,we introduce the operator norm of dual complex matrices induced by the p-norm of dual complex vectors,and give expressions of three important operator norms of dual complex matrices.
文摘针对α稳定分布噪声环境下的自适应滤波问题,提出一种新的基于梯度范数的变步长归一化最小平均p范数(variable step-size normalized least mean p-norm,VSS-NLMP)算法。该算法首先对梯度矢量进行加权平滑,以减小梯度噪声的影响,然后利用梯度矢量能够跟踪自适应过程的均方偏差这一特点,利用梯度矢量的欧氏范数控制步长的变化。给出了新算法的迭代过程,然后对其收敛性进行分析,仿真结果表明本算法较现有变步长NLMP算法有更好的性能。
文摘在强脉冲噪声干扰背景中,核递归最小二乘(Kernel Recursive Least Square,KRLS)算法和核递归最大相关熵(Kernel Recursive Maximum Correntropy,KRMC)算法对非线性信号预测性能严重退化,对此提出一种核递归最小平均P范数(Kernel Recursive Least Mean P-norm,KRLMP)算法。首先运用核方法将输入数据映射到再生核希尔伯特空间(Reproducing Kernnel Hilbert Space,RKHS)。其次基于最小P范数准则和正则化方法,推导得到自适应滤波器的最佳权向量,其降低了非高斯脉冲和样本量少的影响。然后利用矩阵求逆理论,推导得到矩阵的递归公式。最后利用核技巧得到在输入空间高效计算的滤波器输出和算法的迭代公式。α稳定分布噪声背景下Mackey-Glass时间序列预测的仿真结果表明:KRLMP算法与KRLS算法和KRMC算法相比,抗脉冲噪声能力强,鲁棒性好。
文摘Few study gives guidance to design weighting filters according to the frequency weighting factors,and the additional evaluation method of automotive ride comfort is not made good use of in some countries.Based on the regularities of the weighting factors,a method is proposed and the vertical and horizontal weighting filters are developed.The whole frequency range is divided several times into two parts with respective regularity.For each division,a parallel filter constituted by a low-and a high-pass filter with the same cutoff frequency and the quality factor is utilized to achieve section factors.The cascading of these parallel filters obtains entire factors.These filters own a high order.But,low order filters are preferred in some applications.The bilinear transformation method and the least P-norm optimal infinite impulse response（IIR） filter design method are employed to develop low order filters to approximate the weightings in the standard.In addition,with the window method,the linear phase finite impulse response（FIR） filter is designed to keep the signal from distorting and to obtain the staircase weighting.For the same case,the traditional method produces 0.330 7 m · s^–2 weighted root mean square（r.m.s.） acceleration and the filtering method gives 0.311 9 m · s^–2 r.m.s.The fourth order filter for approximation of vertical weighting obtains 0.313 9 m · s^–2 r.m.s.Crest factors of the acceleration signal weighted by the weighting filter and the fourth order filter are 3.002 7 and 3.011 1,respectively.This paper proposes several methods to design frequency weighting filters for automotive ride comfort evaluation,and these developed weighting filters are effective.
