Event-triggered distributed state estimation for a class of time-varying systems over sensor networks with redundant channels

This paper is concerned with the distributed state estimation problem for a class of time-varying systems over sensor networks. An event-triggered communication scheme is utilized to save the constrained computation resource and network bandwidth while preserving the desired performance. The measurements on each node are transmitted to the estimators only when a certain triggering condition is satisfied. Moreover, in order to improve the reliability of data transmission services, we exploit redundant communication channels during the transmission process. The purpose of this paper is to design a set of time-varying state estimators such that the dynamics of the state estimation error satisfies the average H_∞ performance constraints. The specific gains of the estimator can be obtained by calculating a series of recursive linear matrix inequalities (RLMIs). Finally, a simulation example is presented to show the effectiveness of the state estimation method proposed in this paper.     

Event-triggered state estimation for Markovian jumping impulsive neural networks with interval time-varying delays

This paper investigates the event-triggered state estimation problem of Markovian jumping impulsive neural networks with interval time-varying delays. The purpose is to design a state estimator to estimate system states through available output measurements. In the neural networks, there are a set of modes, which are determined by Markov chain. A Markovian jumping time-delay impulsive neural networks model is employed to describe the event-triggered scheme and the network- related behaviour, such as transmission delay, data package dropout and disorder. The proposed event-triggered scheme is used to determine whether the sampled state information should be transmitted. The discrete delays are assumed to be time-varying and belong to a given interval, which means that the lower and upper bounds of interval time-varying delays are available. First, we design a state observer to estimate the neuron states. Second, based on a novel Lyapunov-Krasovskii functional (LKF) with triple-integral terms and using an improved inequality, several sufficient conditions are derived. The derived conditions are formulated in terms of a set of linear matrix inequalities , under which the estimation error system is globally asymptotically stable in the mean square sense. Finally, numerical examples are given to show the effectiveness and superiority of the results.     

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.     

大规模不一致传感网络环境带宽受限下的分布式状态估计

无线传感器网络环境下受限于能量和带宽,传感器的观测往往需要经过量化后才发送,针对大规模不一致传感网络环境且带宽受限下的分布式状态估计,探讨了量化比特分配和估计性能评估问题。首先给出一种二进制概率量化方案,并基于量化观测构造线性无偏量化估计器。然后,考虑一个总的传输比特率限制下,得到了传感器的最优量化比特率及比特分配方案,由其信噪比(SNR)和总带宽确定。同时,对提出的量化估计器的均方误差上界进行了分析,发现其与理论下界仅相差一个小常数因子。最后,仿真结果表明,相比于一般的均匀比特分配,文中所提出的最优比特分配方案估计性能更优。     

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.     

Event-triggered state estimation for T-S fuzzy affine systems based on piecewise Lyapunov-Krasovskii functionals

This paper investigates the problem of event-triggered ${\rm H}_\infty$ state estimation for Takagi-Sugeno (T-S) fuzzy affine systems. The objective is to design an event-triggered scheme and an observer such that the resulting estimation error system is asymptotically stable with a prescribed ${\rm H}_{\infty}$ performance and at the same time unnecessary output measurement transmission can be reduced. First, an event-triggered scheme is proposed to determine whether the sampled measurements should be transmitted or not. The output measurements, which trigger the condition, are supposed to suffer a network-induced time-varying and bounded delay before arriving at the observer. Then, by adopting the input delay method, the estimation error system can be reformulated as a piecewise delay system. Based on the piecewise Lyapunov-Krasovskii functional and the Finsler''s lemma, the event-triggered ${\rm H}_{\infty}$ observer design method is developed. Moreover, an algorithm is proposed to co-design the observer gains and the event-triggering parameters to guarantee that the estimation error system is asymptotically stable with a given disturbance attenuation level and the signal transmission rate is reduced as much as possible. Simulation studies are given to show the effectiveness of the proposed method.     

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.     

State estimation for a class of discrete nonlinear systems with randomly occurring uncertainties and distributed sensor delays

In this paper, the state estimation problem is investigated for a class of discrete nonlinear systems with randomly occurring uncertainties and distributed sensor delays. The norm-bounded uncertainties enter into the system in a randomly way, and such randomly occurring uncertainties (ROUs) obey certain Bernoulli distributed white noise sequence with known conditional probability. By constructing a new Lyapunov–Krasovskii functional, sufficient conditions are proposed to guarantee the convergence of the estimation error for all discrete time-varying delays, ROUs and distributed sensor delays. Subsequently, the explicit form of the estimator parameter is derived by solving two linear matrix inequalities (LMIs) which can be easily tested by using standard numerical software. Finally, a simulation example is given to illustrate the feasibility and effectiveness of the proposed estimation scheme.     

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.     

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.     

Stochastic sensor activation for distributed state estimation over a sensor network

We consider distributed state estimation over a resource-limited wireless sensor network. A stochastic sensor activation scheme is introduced to reduce the sensor energy consumption in communications, under which each sensor is activated with a certain probability. When the sensor is activated, it observes the target state and exchanges its estimate of the target state with its neighbors; otherwise, it only receives the estimates from its neighbors. An optimal estimator is designed for each sensor by minimizing its mean-squared estimation error. An upper and a lower bound of the limiting estimation error covariance are obtained. A method of selecting the consensus gain and a lower bound of the activating probability is also provided.     

Two triggered information transmission algorithms for distributed moving horizon state estimation

In this work, we consider the reduction of information transmission frequency of distributed moving horizon estimation (DMHE) for a class of nonlinear systems in which interacting subsystems exchange information with each other through a shared communication network. Specifically, algorithms based on two event-triggered methods are proposed to reduce the number of information transmissions between the subsystems in a DMHE scheme. In the first algorithm, a subsystem sends out its current information when a triggering condition based on the difference between the current state estimate and a previously transmitted one is satisfied; in the second algorithm, the transmission of information from a subsystem to other subsystems is triggered by the difference between the current measurement of the output and its derivatives and a previously transmitted measurement. In order to ensure the convergence and ultimate boundedness of the estimation error, we also propose to redesign the local moving horizon estimator of a subsystem to account for the possible lack of state updates from other subsystems explicitly. A chemical process is utilized to demonstrate the applicability and performance of the proposed approaches.     

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.     

A new approach to distributed fusion filtering for networked systems with random parameter matrices and correlated noises

This paper is concerned with the distributed filtering problem for a class of discrete-time stochastic systems over a sensor network with a given topology. The system presents the following main features: (i) random parameter matrices in both the state and observation equations are considered; and (ii) the process and measurement noises are one-step autocorrelated and two-step cross-correlated. The state estimation is performed in two stages. At the first stage, through an innovation approach, intermediate distributed least-squares linear filtering estimators are obtained at each sensor node by processing available output measurements not only from the sensor itself but also from its neighboring sensors according to the network topology. At the second stage, noting that at each sampling time not only the measurement but also an intermediate estimator is available at each sensor, attention is focused on the design of distributed filtering estimators as the least-squares matrix-weighted linear combination of the intermediate estimators within its neighborhood. The accuracy of both intermediate and distributed estimators, which is measured by the error covariance matrices, is examined by a numerical simulation example where a four-sensor network is considered. The example illustrates the applicability of the proposed results to a linear networked system with state-dependent multiplicative noise and different network-induced stochastic uncertainties in the measurements; more specifically, sensor gain degradation, missing measurements and multiplicative observation noises are considered as particular cases of the proposed observation model.     

一种带波门修正的事件触发机制及其在光电探测网中的应用

本文针对一类通信资源有限的集中式目标状态估计问题进行了研究, 提出一种带波门修正的事件触发机制.当事件触发条件不满足时, 相应探测器按通信系统设计带宽发送完整量测新息至融合中心.当事件触发条件满足时, 相应探测器将量化量测新息发送给融合中心.减少数据传输量, 减轻通信系统的负担.随后推导机制下的融合中心最小均方误差状态估计算法并对其性能进行了理论分析.最后给出一个光电探测网的应用算例, 表明了其在工程应用中的有效性及可行性.     

Stochastic control of processes having moving boundaries—An experimental study

A general state estimator requiring only discrete time measurements has been developed for nonlinear distributed parameter systems having moving boundaries. The state estimator has been combined with an optimal linear-quadratic feedback controller to provide a stochastic feedback control scheme for this class of problem. Both the state estimation and control algorithms were implemented in real time for a laboratory casting process and were found to perform well. The state estimation scheme would seem to hold the most interest for industrial applications.     

传感器网络中的分布式滚动时域状态估计

利用分布式滚动时域方法对无线传感器网络的状态估计问题进行研究,给出了基于量化测量值的滚动时域估计算法。在无线传感器网络的环境下处理分布式状态估计问题时,减少通信的成本是非常重要的一个环节,需要将观测值量化后再传送。以往的滚动时域估计方法无法处理量化观测值的状态估计问题,而本文的方法考虑了最严格的观测值量化情况即传感器只发送一个比特至融合中心的状态估计问题。与其它传感器网络中的状态估计方法相比,该方法减少了每一步的计算量。仿真结果验证了该算法的有效性。     

Decentralized robust set-valued state estimation in networked multiple sensor systems

This paper addresses a decentralized robust set-valued state estimation problem for a class of uncertain systems via a data-rate constrained sensor network. The uncertainties of the systems satisfy an energy-type constraint known as an integral quadratic constraint. The sensor network consists of spatially distributed sensors and a fusion center where set-valued state estimation is carried out. The communications from the sensors to the fusion center are through data-rate constrained communication channels. We propose a state estimation scheme which involves coders that are implemented in the sensors, and a decoder–estimator that is located at the fusion center. Their construction is based on the robust Kalman filtering techniques. The robust set-valued state estimation results of this paper involve the solution of a jump Riccati differential equation and the solution of a set of jump state equations.     

Distributed bounded-error state estimation based on practical robust positive invariance

We propose a state estimator for linear discrete-time systems composed by coupled subsystems affected by bounded disturbances. The architecture is distributed in the sense that each subsystem is equipped with a local state estimator that exploits suitable pieces of information from parent subsystems. Furthermore, each local estimator reconstructs the state of the corresponding subsystem only. Different from methods based on moving horizon estimation, our approach does not require the online solution to optimisation problems. Our state estimation scheme, which is based on the notion of practical robust positive invariance, also guarantees satisfaction of constraints on local estimation errors and it can be updated with a limited computational effort when subsystems are added or removed.     

State estimation for complex systems with randomly occurring nonlinearities and randomly missing measurements

This paper is concerned with the state estimation problem for the complex networked systems with randomly occurring nonlinearities and randomly missing measurements. The nonlinearities are included to describe the phenomena of nonlinear disturbances which exist in the network and may occur in a probabilistic way. Considering the fact that probabilistic data missing may occur in the process of information transmission, we introduce the randomly data missing into the sensor measurements. The aim of this paper is to design a state estimator to estimate the true states of the considered complex network through the available output measurements. By using a Lyapunov functional and some stochastic analysis techniques, sufficient criteria are obtained in the form of linear matrix inequalities under which the estimation error dynamics is globally asymptotically stable in the mean square. Furthermore, the state estimator gain is also obtained. Finally, a numerical example is employed to illustrate the effectiveness of the proposed state estimation conditions.