State estimation for two‐dimensional complex networks with randomly occurring nonlinearities and randomly varying sensor delays

This paper is concerned with the state estimation problem for two‐dimensional (2D) complex networks with randomly occurring nonlinearities and randomly varying sensor delays. To describe the fact that measurement delays may occur in a probabilistic way, the randomly varying sensor delays are introduced in the delayed sensor measurements. The randomly occurring nonlinearity, on the other hand, is included to account for the phenomenon of nonlinear disturbances appearing in a random fashion that is governed by a Bernoulli distributed white sequence with known conditional probability. The stochastic Brownian motions are also considered, which enter into not only the coupling terms of the complex networks but also the measurements of the output systems. Through available actual network measurements, a state estimator is designed to estimate the true states of the considered 2D complex networks. By utilizing an energy‐like function, the Kronecker product and some stochastic analysis techniques, several sufficient criteria are established in terms of matrix inequalities under which the 2D estimation error dynamics is globally asymptotically stable in the mean square. Furthermore, the explicit expression of the estimator gains is also characterized. Finally, a numerical example is provided to demonstrate the effectiveness of the design method proposed in this paper. Copyright © 2012 John Wiley & Sons, Ltd.     

Recursive filtering for state‐saturated systems with randomly occurring nonlinearities and missing measurements

This paper deals with the filtering problem for a class of discrete‐time state‐saturated systems subject to randomly occurring nonlinearities and missing measurements. A set of mutually independent Bernoulli random variables is used to describe the random occurrence of the missing measurements. Due to the simultaneous consideration of the state saturation, the randomly occurring nonlinearities, and the missing measurements, it is extremely hard to calculate the actual filtering error covariance in a closed form. As such, the objective of this paper is to construct an upper bound for the filtering error covariance and then design the filter parameters to minimize such an upper bound. The performance of the proposed filters is analyzed in terms of boundedness and monotonicity. Specially, we have shown that the minimum upper bound is always bounded under a mild assumption. Moreover, the relationship between the estimator performance and the arrival probability of the measurements is discussed. A numerical simulation is used to demonstrate the effectiveness of the filtering method.     

state estimation with fading measurements,randomly varying nonlinearities and probabilistic distributed delays

In this paper, the state estimation problem is investigated for a class of discrete‐time stochastic systems in simultaneous presence of three network‐induced phenomena, namely, fading measurements, randomly varying nonlinearities and probabilistic distributed delays. The channel fading is characterized by the ?th‐order Rice fading model whose coefficients are mutually independent random variables with given probability density functions. Two sequences of random variables obeying the Bernoulli distribution are utilized to govern the randomly varying nonlinearities and probabilistic distributed delays. The purpose of the problem addressed is to design an state estimator such that the dynamics of the estimation errors is stochastically stable and the prespecified disturbance rejection attenuation level is guaranteed. Through intensive stochastic analysis, sufficient conditions are established under which the addressed state estimation problem is recast as a convex optimization one that can be solved via the semi‐definite program method. Finally, a simulation example is provided to show the usefulness of the proposed state estimation scheme. Copyright © 2014 John Wiley & Sons, Ltd.     

Dissipative control for state-saturated discrete time-varying systems with randomly occurring nonlinearities and missing measurements

In this paper, the dissipative control problem is investigated for a class of discrete time-varying systems with simultaneous presence of state saturations, randomly occurring nonlinearities as well as multiple missing measurements. In order to render more practical significance of the system model, some Bernoulli distributed white sequences with known conditional probabilities are adopted to describe the phenomena of the randomly occurring nonlinearities and the multiple missing measurements. The purpose of the addressed problem is to design a time-varying output-feedback controller such that the dissipativity performance index is guaranteed over a given finite-horizon. By introducing a free matrix with its infinity norm less than or equal to 1, the system state is bounded by a convex hull so that some sufficient conditions can be obtained in the form of recursive nonlinear matrix inequalities. A novel controller design algorithm is then developed to deal with the recursive nonlinear matrix inequalities. Furthermore, the obtained results are extended to the case when the state saturation is partial. Two numerical simulation examples are provided to demonstrate the effectiveness and applicability of the proposed controller design approach.     

带随机量测时滞和随机丢包的改进无迹卡尔曼滤波

经典卡尔曼滤波要求量测值可实时获取,且仅适用于线性系统.然而,在工程实际应用中,系统多为非线性系统,量测值也会发生滞后或者丢失等现象,此时经典卡尔曼滤波已不适用.因此,本文针对一类带有随机量测一步时滞和随机丢包的非线性离散系统的状态估计问题,用两个满足伯努利分布的独立随机变量来描述随机量测一步滞后和随机丢包的现象.当量测丢失时,用量测值的一步预测值来代替零输入进行补偿.在此基础上应用正交投影理论和无迹变换的方法提出了一种改进的无迹卡尔曼滤波算法.最后,通过仿真例子验证在考虑随机量测一步时滞和随机丢包的情况下,所提出的改进算法相比于经典无迹卡尔曼滤波算法具有更高的精度.     

复杂网络的事件驱动故障估计

针对一类非线性耦合的复杂网络系统，提出了一种基于复杂网络估计器的近似最优故障估计方法.首先将复杂网络的状态与故障进行增广，然后对增广后的状态和故障进行了联合状态估计.为了处理多信号传输可能发生的数据冲突，采用了事件驱动的方法使复杂网络的输出传输至远程估计器.通过递推矩阵方程方法给出了估计误差协方差矩阵的上界，并通过设计估计器参数使得该上界在迹的意义下最小.最后，通过仿真例子验证了所提联合估计方案的可行性和有效性.     

Kalman filter-based identification for systems with randomly missing measurements in a network environment

We consider the problem of parameter estimation and output estimation for systems in a transmission control protocol (TCP) based network environment. As a result of networked-induced time delays and packet loss, the input and output data are inevitably subject to randomly missing data. Based on the available incomplete data, we first model the input and output missing data as two separate Bernoulli processes characterised by probabilities of missing data, then a missing output estimator is designed, and finally we develop a recursive algorithm for parameter estimation by modifying the Kalman filter-based algorithm. Under the stochastic framework, convergence properties of both the parameter estimation and output estimation are established. Simulation results illustrate the effectiveness of the proposed algorithms.     

Optimal state estimation using randomly delayed measurements without time stamping

This paper studies an optimal state estimation (Kalman filtering) problem under the assumption that output measurements are subject to random time delays caused by network transmissions without time stamping. We first propose a random time delay model which mimics many practical digital network systems. We then study the so‐called unbiased, uniformly bounded linear state estimators and show that the estimator structure is given based on the average of all received measurements at each time for different maximum time delays. The estimator gains can be derived by solving a set of recursive discrete‐time Riccati equations. The estimator is guaranteed to be optimal in the sense that it is unbiased with uniformly bounded estimation error covariance. A simulation example shows the effectiveness of the proposed algorithm. Copyright © 2013 John Wiley & Sons, Ltd.     

State Estimation for Coupled Uncertain Stochastic Networks With Missing Measurements and Time-Varying Delays: The Discrete-Time Case

This paper is concerned with the problem of state estimation for a class of discrete-time coupled uncertain stochastic complex networks with missing measurements and time-varying delay. The parameter uncertainties are assumed to be norm-bounded and enter into both the network state and the network output. The stochastic Brownian motions affect not only the coupling term of the network but also the overall network dynamics. The nonlinear terms that satisfy the usual Lipschitz conditions exist in both the state and measurement equations. Through available output measurements described by a binary switching sequence that obeys a conditional probability distribution, we aim to design a state estimator to estimate the network states such that, for all admissible parameter uncertainties and time-varying delays, the dynamics of the estimation error is guaranteed to be globally exponentially stable in the mean square. By employing the Lyapunov functional method combined with the stochastic analysis approach, several delay-dependent criteria are established that ensure the existence of the desired estimator gains, and then the explicit expression of such estimator gains is characterized in terms of the solution to certain linear matrix inequalities (LMIs). Two numerical examples are exploited to illustrate the effectiveness of the proposed estimator design schemes.     

Semi-supervised learning with density-ratio estimation

In this paper we study statistical properties of semi-supervised learning, which is considered to be an important problem in the field of machine learning. In standard supervised learning only labeled data is observed, and classification and regression problems are formalized as supervised learning. On the other hand, in semi-supervised learning, unlabeled data is also obtained in addition to labeled data. Hence, the ability to exploit unlabeled data is important to improve prediction accuracy in semi-supervised learning. This problem is regarded as a semiparametric estimation problem with missing data. Under discriminative probabilistic models, it was considered that unlabeled data is useless to improve the estimation accuracy. Recently, the weighted estimator using unlabeled data achieves a better prediction accuracy compared to the learning method using only labeled data, especially when the discriminative probabilistic model is misspecified. That is, improvement under the semiparametric model with missing data is possible when the semiparametric model is misspecified. In this paper, we apply the density-ratio estimator to obtain the weight function in semi-supervised learning. Our approach is advantageous because the proposed estimator does not require well-specified probabilistic models for the probability of the unlabeled data. Based on statistical asymptotic theory, we prove that the estimation accuracy of our method outperforms supervised learning using only labeled data. Some numerical experiments present the usefulness of our methods.     

Synchronization and State Estimation for Discrete-Time Complex Networks With Distributed Delays

In this paper, a synchronization problem is investigated for an array of coupled complex discrete-time networks with the simultaneous presence of both the discrete and distributed time delays. The complex networks addressed which include neural and social networks as special cases are quite general. Rather than the commonly used Lipschitz-type function, a more general sector-like nonlinear function is employed to describe the nonlinearities existing in the network. The distributed infinite time delays in the discrete-time domain are first defined. By utilizing a novel Lyapunov–Krasovskii functional and the Kronecker product, it is shown that the addressed discrete-time complex network with distributed delays is synchronized if certain linear matrix inequalities (LMIs) are feasible. The state estimation problem is then studied for the same complex network, where the purpose is to design a state estimator to estimate the network states through available output measurements such that, for all admissible discrete and distributed delays, the dynamics of the estimation error is guaranteed to be globally asymptotically stable. Again, an LMI approach is developed for the state estimation problem. Two simulation examples are provided to show the usefulness of the proposed global synchronization and state estimation conditions. It is worth pointing out that our main results are valid even if the nominal subsystems within the network are unstable.      

Distributed consensus estimation for diffusion systems with missing measurements over sensor networks

In this paper, the problem of distributed consensus estimation with randomly missing measurements is investigated for a diffusion system over the sensor network. A random variable, the probability of which is known a priori, is used to model the randomly missing phenomena for each sensor. The aim of the addressed estimation problem is to design distributed consensus estimators depending on the neighbouring information such that, for all random measurement missing, the estimation error systems are guaranteed to be globally asymptotically stable in the mean square. By using Lyapunov functional method and the stochastic analysis approach, the sufficient conditions are derived for the convergence of the estimation error systems. Finally, a numerical example is given to demonstrate the effectiveness of the proposed distributed consensus estimator design scheme.     

Finite‐horizon fault estimation for time‐varying systems with multiple fading measurements under torus‐event–based protocols

In this paper, the issue of the finite‐horizon H_∞ fault estimation is dealt with for a class of discrete time‐varying systems subject to randomly occurring faults and multiple fading measurements. The missing phenomena may occur in a random way from different sensors, which is represented by an individual stochastic variable meeting a certain probability distribution. Furthermore, in order to alleviate the communication burden, the torus‐event–based protocols are adopted to schedule the data transmissions only when some significant events occur. Our aim of the presented issue is to estimate the fault such that, with multiple fading measurements via the received information governed by torus‐event–based protocols, the H_∞ index is satisfied over a given finite horizon. Sufficient conditions are obtained for the desired time‐varying estimator in terms of the technique of stochastic analysis and the methods of completing squares. The desired estimator gains are calculated by working out two backward recursive Riccati difference equations. Finally, a numerical simulation is given to verify the usefulness of our designed fault estimation approach.     

Distributed state estimation for uncertain sensor networks with mixed time delays subject to sensor saturations

In this paper, the distributed state estimation problem is investigated for a class of uncertain sensor networks. The target plant is described by a set of uncertain difference equations with both discrete-time and infinite distributed delays, where two random variables are introduced to account for the randomly occurring nonlinearities. The sensor measurement outputs are subject to randomly occurring sensor saturations due to the physical limitations of the sensors. Through available output measurements from each individual sensor and its neighboring sensors, this paper aims to design distributed state estimators to approximate the states of the target plant in a distributed way. Sufficient conditions are presented which not only guarantee the estimation error systems to be globally asymptotically stable in the mean square sense but also ensure the existence of the desired estimator gains.     

Robust state estimation for uncertain discrete-time stochastic systems with missing measurements

In this paper, results of robust estimation of Zhou (2010a) are extended to state estimation with missing measurements. A new procedure is derived which inherits the main properties of that of Zhou (2010a). In this extension, a covariance matrix used in the recursions is replaced by its estimate which makes its asymptotic property investigation mathematically difficult. Though introducing a monotonic function and using the so-called squeeze rule, this new robust estimator is proved to converge to a stable system. Numerical simulation results indicate that the proposed estimator may have an estimation accuracy better than the estimator of Wang, Yang, Daniel, and Liu (2005).     

Distributed fusion filters from uncertain measured outputs in sensor networks with random packet losses

This paper addresses the distributed fusion filtering problem for discrete-time random signals from measured outputs perturbed by random parameter matrices and correlated additive noises. These measurements are obtained by a sensor network with a given topology, where random packet dropouts occur during the data transmission through the different network communication channels. The distributed fusion estimation is accomplished in two phases. Firstly, by an innovation approach and using the last observation that successfully arrived if a packet is lost, a preliminary distributed least-squares estimator is designed at each sensor node using its own measurements and those from its neighbors. Secondly, every sensor collects the preliminary filters that are successfully received from its neighbors and fuses this information with its own one to generate the least-squares linear matrix-weighted distributed fusion estimator. The accuracy of the proposed estimators, which is measured by the estimation error covariances, is examined by a numerical simulation example.     

Observer‐based H∞ control for systems with repeated scalar nonlinearities and multiple packet losses

This paper is concerned with the H_∞ control problem for a class of systems with repeated scalar nonlinearities and multiple missing measurements. The nonlinear system is described by a discrete‐time state equation involving a repeated scalar nonlinearity, which typically appears in recurrent neural networks. The measurement missing phenomenon is assumed to occur, simultaneously, in the communication channels from the sensor to the controller and from the controller to the actuator, where the missing probability for each sensor/actuator is governed by an individual random variable satisfying a certain probabilistic distribution in the interval [0 1]. Attention is focused on the analysis and design of an observer‐based feedback controller such that the closed‐loop control system is stochastically stable and preserves a guaranteed H_∞ performance. Sufficient conditions are obtained for the existence of admissible controllers. It is shown that the controller design problem under consideration is solvable if certain linear matrix inequalities (LMIs) are feasible. Three examples are provided to illustrate the effectiveness of the developed theoretical results. Copyright © 2009 John Wiley & Sons, Ltd.     

Gaussian-consensus filter for nonlinear systems with randomly delayed measurements in sensor networks

This paper presents the decentralized state estimation problem of discrete-time nonlinear systems with randomly delayed measurements in sensor networks. In this problem, measurement data from the sensor network is sent to a remote processing network via data transmission network, with random measurement delays obeying a Markov chain. Here, we present the Gaussian-consensus filter (GCF) to pursue a tradeoff between estimate accuracy and computing time. It includes a novel Gaussian approximated filter with estimated delay probability (GEDPF) online in the sense of minimizing the estimate error covariance in each local processing unit (PU), and a consensus strategy among PUs in processing network to give a fast decentralized fusion. A numerical example with different measurement delays is simulated to validate the proposed method.     

量测随机延迟下带相关乘性噪声的非线性系统分布式估计

本文提出了乘性噪声和加性噪声相关下的量测随机延迟非线性系统分布式状态估计.在所考虑系统中,相关状态被多传感器簇构成的传感器网所观测.所得理想量测被传送到远程分布式处理网,并伴随服从一阶马尔可夫过程的随机延迟.在此基础上,本文提出了分布式高斯信息滤波(distributed Gaussian-information filter,DGIF),来实现估计精度与计算时间的折中.在单处理节点/单元中,以估计误差协方差最小化为准则,设计了相应的高斯递推滤波,并实现了延迟概率的在线递推估计.进一步地,在分布式处理网中,基于非线性量测方程的统计线性回归,结合一致性算法,给出了一种分布式信息滤波形式,有效实现了分布式融合.分别在单处理单元和分布式处理网中仿真验证了所提算法的有效性.     

能量和带宽受限下的分布式一致性融合估计器

针对网络化多传感器分布式估计中传感器能量和通信网络带宽约束问题,提出一种基于降低发送频率和数据压缩降维的分布式一致性融合估计算法.为了满足通信网络带宽要求,各传感器节点直接选取局部估计信号的部分分量进行传输;与此同时,各节点随机间歇式发送数据包到其他节点来节省能量.在给定一致性权重下,建立以一致性估计器增益为决策变量,以所有传感器节点有限时域下状态融合估计误差协方差矩阵的迹的和为代价函数的优化问题,基于Lyapunov稳定性理论给出使得融合估计误差在无噪声时渐近稳定的一致性估计器增益存在的充分条件,并通过最小化代价函数的上界得到一组次优的一致性估计器增益值.最后,通过算例仿真验证算法的有效性.