时变系统遗忘因子最小二乘法的有界性收敛性

利用随机过程理论研究了遗忘因子最小二乘法（FFLS）的有界收敛性，给出了参数估计误差的上界，分析表明：i)对于时不变确定性系统；FFLS算法产生的参数估计以指数速度收敛于真参数；ii)对于时不变随机系统，FFLS算法给出界均方估计误差，iii)对于时变随机系统，FFLS算法可以跟踪时变参数，且跟踪误差有界。     

时变系统遗忘因子最小二乘法的有界收敛性

利用随机过程理论研究了遗忘因子最小二乘法 (FFLS)的有界收敛性, 给出了参数估计误差的上界. 分析表明: i)对于时不变确定性系统, FFLS算法产生的参数估计以指数速度收敛于真参数; ii)对于时不变随机系统, FFLS算法给出有界均方估计误差; iii)对于时变随机系统, FFLS算法可以跟踪时变参数, 且跟踪误差有界.     

时变参数遗忘梯度估计算法的收敛性

提出了时变随机系统的遗忘梯度辨识算法,并运用随机过程理论研究了算法的收敛 性.分析表明,遗忘梯度算法的性能类似于遗忘因子最小二乘法,可以跟踪时变参数,但计算量 要小得多,且数据的平稳性可以减小参数估计误差上界和提高辨识精度.阐述了最佳遗忘因子 的选择方法,以获得最小参数估计上界.对于确定性时不变系统,遗忘梯度算法是指数速度收 敛的;对于时变或时不变随机系统,遗忘梯度算法的参数估计误差一致有上界.     

时变系统有限数据窗最小二乘辨识的有界收敛性

利用随机过程理论证明了有限数据窗最小二乘法的有界收敛性,给出了参数估计误差 上界的计算公式,阐述了获得最小均方参数估计误差上界时数据窗长度的选择方法.分析表明, 对于时不变随机系统,数据窗长度越大,均方参数估计误差上界越小;对于确定性时变系统,数 据窗长度越小,均方参数估计误差上界越小.因此,对于时变随机系统,一个折中方案是寻求一 个最佳数据窗长度,以使均方参数估计误差最小.该文的研究成果对于提高辨识算法的实际应 用效果有重要意义.     

辅助变量最小二乘辨识的均方收敛性

利用随机过程理论,首次证明了递推辅助变量最小二乘（RIVLS）的收敛性,研究了RIVLS算法的收敛速率,给出估算RIVLS算法均方参数估计误差上界的计算公式。分析表明,当辅助矩阵与信息矩阵的乘积是非奇异性,且关于辅助向量的弱持续激励条件成立时,均方参数估计误差以（1／t）的速率收敛于零。这一研究结果对于提高RIVLS算法的实际应用效果具有重要意义。数字仿真例子表明了该结论的正确性。     

辅助变量最小二乘辨识的均方收敛性

利用随机过程理论,首次证明了递推辅助变量最小二乘(RIVLS)的收敛性,研究了RIVLS算法的收敛速率,给出估算RIVLS算法均方参数估计误差上界的计算公式.分析表明,当辅助矩阵与信息矩阵的乘积是非奇异阵,且关于辅助向量的弱持续激励条件成立时,均方参数估计误差以(1/t)的速率收敛于零.这一研究结果对于提高RIVLS算法的实际应用效果具有重要意义.数字仿真例子表明了该结论的正确性.     

关于鞅超收敛定理与遗忘因子最小二乘算法的收敛性分析

鞅超收敛定理是研究随机时变系统辨识算法有界收敛性的一个有效数学工具,它是鞅收益是在随机时变系统中的推广。文「１」用它证明了遗忘因子最小二乘算法参数估计误差的有界收敛性,但是文「１」假设系统的理各态遍历的,且协方差阵是用它的数学期望代替的,所得到的结果是近似的。而本文精确地给出了协方差阵的上下界,改进了文「１」的结果。     

一种改进变步长因子LMS算法的研究

传统的LMS算法,由于其步长因子μ是事先指定的固定值,因而在迭代过程中不能随着估计误差e（n）来进行相应的调整,所以其收敛性完全由初始条件和步长决定。为了改变这种状况,文章提出了一种步长因子μ（n）随时间变化的LMS算法,其收敛速度快于LMS和NLMS,具有较小的失调,将本算法应用于自适应预测系统,Matlab仿真实验结果与理论分析一致。     

衰减激励条件下最小均方算法的收敛性

给出了衰减激励信号的定义,并在衰减激励条件下,利用随机过程理论,研究了随机系统最小均方算法的收敛速率,阐述了参数估计误差收敛时,衰减指数和算法中设计参变量 (收敛因子或步长 )的选择方法.分析表明:在衰减激励条件下,最小均方算法也具有良好的性能:当衰减指数和设计参变量满足一定条件时,则参数估计误差一致收敛于零.     

一种改进的LMS/F组合算法及其在同址干扰抵消中的应用

在研究最小均方算法LMS(Least Mean Squre)、最小四阶算法LMF(Least Mean Fourth)和LMS/F组合算法的基础上,引入修正因子γ对LMS/F组合算法进行改进。改进的LMS/F组合算法在保持LMS/F组合算法优良的收敛精度和稳定性的基础上,进一步提高了收敛速度和对时变系统的跟踪特性。改进的算法参数调整简单、高效且运算量小,仿真结果与理论分析相一致,证实了该算法的优异性能。     

Robust estimation for discrete time‐varying systems with limited communication capacity

In this paper, we consider the state estimation problem for linear discrete time‐varying systems subject to limited communication capacity which includes measurement quantization, random transmission delay and data‐packet dropouts. Based on transforming the three communication limitations into the system with norm‐bounded uncertainties and stochastic matrices, we design a robust filter such that, for all the communication limitations, the error state of the filtering process is mean square bounded. An upper bound on the variance of the state estimation error is first found, and then, a robust filter is derived by minimizing the prescribed upper bound in the sense of the matrix norm. It is shown that the desired filter can be obtained in terms of the solutions to two Riccati‐like difference equations which also provide a recursive algorithm suitable for online computation. A simulation example is presented to demonstrate the effectiveness and applicability of the proposed algorithm. Copyright © 2010 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society     

Stochastic stability of the unscented Kalman filter with intermittent observations

In this paper, the stochastic stability of the discrete-time unscented Kalman filter for general nonlinear stochastic systems with intermittent observations is proposed. It is shown that the estimation error remains bounded if the system satisfies some assumptions. And the statistical convergence property of the estimation error covariance is studied, showing the existence of a critical value for the arrival rate of the observations. An upper bound on this expected state error covariance is given. A numerical example is given to illustrate the effectiveness of the techniques developed.     

Least mean square algorithms with Markov regime-switching limit

We analyze the tracking performance of the least mean square (LMS) algorithm for adaptively estimating a time varying parameter that evolves according to a finite state Markov chain. We assume the Markov chain jumps infrequently between the finite states at the same rate of change as the LMS algorithm. We derive mean square estimation error bounds for the tracking error of the LMS algorithm using perturbed Lyapunov function methods. Then combining results in two-time-scale Markov chains with weak convergence methods for stochastic approximation, we derive the limit dynamics satisfied by continuous-time interpolation of the estimates. Unlike most previous analyzes of stochastic approximation algorithms, the limit we obtain is a system of ordinary differential equations with regime switching controlled by a continuous-time Markov chain. Next, to analyze the rate of convergence, we take a continuous-time interpolation of a scaled sequence of the error sequence and derive its diffusion limit. Somewhat remarkably, for correlated regression vectors we obtain a jump Markov diffusion. Finally, two novel examples of the analysis are given for state estimation of hidden Markov models (HMMs) and adaptive interference suppression in wireless code division multiple access (CDMA) networks.     

Iterative Learning Control for Nonlinear Systems: A Bounded‐Error Algorithm

This paper presents a nonlinear iterative learning control (NILC) for nonlinear time‐varying systems. An algorithm of a new strategy for the NILC implementation is proposed. This algorithm ensures that trajectory‐tracking errors of the proposed NILC, when implemented, are bounded by a given error norm bound. A special feature of the algorithm is that the trial‐time interval is finite but not fixed as it is for the other iterative learning algorithms. A sufficient condition for convergence and robustness of the bounded‐error learning procedure is derived. With respect to the bounded‐error and standard learning processes applied to a virtual robot, simulation results are presented in order to verify maximal tracking errors, convergence and applicability of the proposed learning control.     

不确定离散系统的最优鲁棒滤波

本文对一类含有范数有界参数不确定的离散线性系统的滤波问题进行了研究,了有限时域时变以及无限时域时不变两种情形,给出了一个对所有可容许参数不确定都能满足的估计误差方差上界,得到了使得该上界达到最小的最优鲁棒滤波器形式及其存在的充要条件,数值结果表明：当系统存在参数不确定时,本文所得到的滤波器优于标准的Ｋａｌｍａｎ滤波器以及文（４）中的鲁棒滤波器。     

Event-triggered filtering and fault estimation for nonlinear systems with stochastic sensor saturations

This paper is concerned with the filtering problem for a class of nonlinear systems with stochastic sensor saturations and event-triggered measurement transmissions. An event-triggered transmission scheme is proposed with hope to ease the traffic burden and improve the energy efficiency. The measurements are subject to randomly occurring sensor saturations governed by Bernoulli-distributed sequences. Special effort is made to obtain an upper bound of the filtering error covariance in the presence of linearisation errors, stochastic sensor saturations as well as event-triggered transmissions. A filter is designed to minimise the obtained upper bound at each time step by solving two sets of Riccati-like matrix equations, and thus the recursive algorithm is suitable for online computation. Sufficient conditions are established under which the filtering error is exponentially bounded in mean square. The applicability of the presented method is demonstrated by dealing with the fault estimation problem. An illustrative example is exploited to show the effectiveness of the proposed algorithm.