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。     

时变系统最小均方算法的性能分析

在无过程数据平稳性假设和各态遍历等条件下,运用随机过程理论研究了最小方算法（LMS）的有界收敛性,给出了估计误差的上界,论述了LMS算法收敛因子或步长的选择方法,以使参数估计误差上界最小。这对于提高LMS算法的实际应用效果有着重要意义。LMS算法的收敛性分析表明：（1）对于确定性时不变系统,LMS算法是指数速度收敛的;（2）对于确定性时变系统,收敛因子等于1,LMS算法的参数估计误差上界最小;（3）对于时变或不变随机系统,LMS算法的参数估计误差一致有上界。     

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.     

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.     

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。     

M-独立条件下LMS算法的稳定区域

对于著名的最小均方算法,当算法中的输入数据满足M-独立条件时,首先得到了一 个使得最小均方算法指数稳定的充分条件,然后进一步给出了一个确切的步长的取值区域, 证明在此区域内,最小均方算法的估计误差是有界的.     

具有噪声方差及多种网络诱导不确定系统鲁棒Kalman估计

对不确定噪声方差乘性噪声,同时带观测缺失、丢包和一步随机观测滞后三种网络诱导特征的混合不确定网络化系统,应用带虚拟噪声的扩维方法和去随机参数方法,将其转化为带不确定虚拟噪声方差的时变系统.基于极大极小鲁棒估计原理,对带虚拟噪声方差保守上界的最坏情形系统,设计了鲁棒时变和稳态Kalman估值器.对所有容许的不确定性,保证实际Kalman估计误差方差有最小上界.应用扩展的Lyapunov方程方法和矩阵分解方法证明了所设计估值器的鲁棒性.证明了实际和保守估值器的精度关系,以及时变和稳态估值器间的按实现收敛性.应用于F-404航空发动机系统的仿真验证了所提出结果的正确性和有效性.     

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。     

Lyapunov-based adaptive state estimation for a class of nonlinear stochastic systems

This paper is concerned with an adaptive state estimation problem for a class of nonlinear stochastic systems with unknown constant parameters. These nonlinear systems have a linear-in-parameter structure, and the nonlinearity is assumed to be bounded in a Lipschitz-like manner. Using stochastic counterparts of Lyapunov stability theory, we present adaptive state and parameter estimators with ultimately exponentially bounded estimator errors in the sense of mean square for both continuous-time and discrete-time nonlinear stochastic systems. Sufficient conditions are given in terms of the solvability of LMIs. Moreover, we also introduce a suboptimal design approach to optimizing the upper bound of the mean-square error of parameter estimation. This suboptimal design procedure is also realized by LMI computations. By a martingale method, we also show that the related Lyapunov function has a non-negative Lyapunov exponent.     

On the adaptive control of a class of systems with random parameters and disturbances

The adaptive control of discrete time parameter linear stochastic systems with random parameters is investigated. It is shown that systems whose (unknown) autoregressive parameters undergo bounded martingale difference disturbances may be stabilized by the application of the so-called Modified Least Squares adaptive control algorithm. Asymptotically, the sample mean square performance criterion is equal to the one step ahead minimum variance control loss (which equals the prediction error variance when the system parameters are known) plus a term which is bounded by a quantity proportional to the square of the bound on the parameter disturbance. This latter term may be interpreted as the increase in the prediction error variance due to the random parameter variation.     

Variance-constrained filtering for uncertain stochastic systems with missing measurements

In this note, we consider a new filtering problem for linear uncertain discrete-time stochastic systems with missing measurements. The parameter uncertainties are allowed to be norm-bounded and enter into the state matrix. The system measurements may be unavailable (i.e., missing data) at any sample time, and the probability of the occurrence of missing data is assumed to be known. The purpose of this problem is to design a linear filter such that, for all admissible parameter uncertainties and all possible incomplete observations, the error state of the filtering process is mean square bounded, and the steady-state variance of the estimation error of each state is not more than the individual prescribed upper bound. It is shown that, the addressed filtering problem can effectively be solved in terms of the solutions of a couple of algebraic Riccati-like inequalities or linear matrix inequalities. The explicit expression of the desired robust filters is parameterized, and an illustrative numerical example is provided to demonstrate the usefulness and flexibility of the proposed design approach.     

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     

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.     

On minimal error entropy stochastic approximation

Information-theoretic concepts are developed and employed to obtain conditions for a minimax error entropy stochastic approximation algorithm to estimate the state of a non-linear discrete time system baaed on noisy linear measurements of the state. Two recursive suboptimal error entropy estimation procedures are presented along with an upper bound formula for the resulting error entropy. A simple example is utilized to compare the optimal and suboptimal error entropy estimators and the minimum mean Square error linear estimator.     

输出信号量化的双率采样系统参数辨识方法

针对双率采样和信号量化(signal quantization)[BFQB]的控制系统,采用随机重复性试验测量信息,提出基于辅助模型的双率采样量化控制系统辨识方法.分析了在随机重复试验和放松估计误差方差条件下,双率采样量化系统的模型特征并给出了分两步辨识的策略,推导了进行参数辨识所满足的持续激励条件,并给出了基于辅助模型的双率采样量化控制系统量化辨识递推算法;接着分析了所给出量化辨识递推算法的收敛性,得到了双率采样量化系统参数估计误差上界的计算式,最后数字仿真验证了该算法及结论的有效性.