Security distributed state estimation for nonlinear networked systems against DoS attacks

This paper is concerned with security distributed state estimation for nonlinear networked systems against denial‐of‐service attacks. By taking the effects of resource constraints into consideration, an event‐triggered scheme and a quantization mechanism are employed to alleviate the burden of network. A mathematical model of distributed state estimation is constructed for nonlinear networked systems against denial‐of‐service attacks. Sufficient conditions ensuring the exponential stability of the estimation error systems are obtained by utilizing the Lyapunov stability theory. The explicit expressions of the designed state estimators are acquired in terms of the linear matrix inequalities. Finally, a numerical example is used to testify the feasibility of the proposed method.     

Active resilient defense control against false data injection attacks in smart grids

The emerging of false data injection attacks (FDIAs) can fool the traditional detection methods by injecting false data, which has brought huge risks to the security of smart grids. For this reason, a resilient active defense control scheme based on interval observer detection is proposed in this paper to protect smart grids. The proposed active defense highlights the integration of detection and defense against FDIAs in smart girds. First, a dynamic physical grid model under FDIAs is modeled, in which model uncertainty and parameter uncertainty are taken into account. Then, an interval observer-based detection method against FDIAs is proposed, where a detection criteria using interval residual is put forward. Corresponding to the detection results, the resilient defense controller is triggered to defense the FDIAs if the system states are affected by FDIAs. Linear matrix inequality (LMI) approach is applied to design the resilient controller with H_{{\infty }} performance. The system with the resilient defense controller can be robust to FDIAs and the gain of the resilient controller has a certain gain margin. Our active resilient defense approach can be built in real time and show accurate and quick respond to the injected FDIAs. The effectiveness of the proposed defense scheme is verified by the simulation results on an IEEE 30-bus grid system.     

集中式与分布式鲁棒状态融合估计

研究不确定多传感器系统的鲁棒估计问题是多传感器融合估计理论的一个重要研究方向.本文以鲁棒滤波理论为基础,给出了不确定多传感器系统的多胞型描述模型,并利用LMI方法给出集中式鲁棒状态融合估计问题的解,证明了将集中式鲁棒融合估计转化为相同估计性能的分布式融合估计算法的条件.最后给出了分布式不确定多传感器系统的状态融合估计的一个算例.     

On the distributed parameter least-squares state estimation theory

Some results concerning the state estimation problem of distributed-parameter systems corrupted by white, in time, stochastic disturbances and noises are presented. The least-squares technique is adopted throughout. First, the Gauss-Markov theorem is extended to the distributed-parameter ease and a dynamic estimator is derived governing the minimal variance linear unbiased estimate of the state of the system at hand. Second, the innovations approach to least-squares estimation is invoked and the filtering, fixed-interval, fixed-point, and fixed-lag smoothing problems are studied and solved. Finally, the stability properties of the optimal filter derived are studied by employing the controllability and observability properties of the system under consideration. The results of the paper provide new tools for dealing with distributed data, thus substantially enlarging the existing distributed-parameter estimation theory.     

Optimal resilient distributed algorithms for ring election

The problem of electing a leader in a dynamic ring in which processors are permitted to fail and recover during election is discussed. It is shown that &thetas;(n log n+k_r) messages, counting only messages sent by functional processors, are necessary and sufficient for dynamic ring election, where k_r is the number of processor recoveries experienced     

Observer-enhanced distributed moving horizon state estimation subject to communication delays

In this work, we focus on distributed moving horizon estimation (DMHE) of nonlinear systems subject to time-varying communication delays. In particular, a class of nonlinear systems composed of subsystems interacting with each other via their states is considered. In the proposed design, an observer-enhanced moving horizon state estimator (MHE) is designed for each subsystem. The distributed MHEs exchange information via a shared communication network. To handle communication delays, an open-loop state predictor is designed for each subsystem to provide predictions of unavailable subsystem states (due to delays). Based on the predictions, an auxiliary nonlinear observer is used to generate a reference subsystem state estimate for each subsystem. The reference subsystem state estimate is used to formulate a confidence region for the actual subsystem state. The MHE of a subsystem is only allowed to optimize its subsystem state estimate within the corresponding confidence region. Under the assumption that there is an upper bound on the time-varying delays, the proposed DMHE is proved to give decreasing and ultimately bounded estimation error. The theoretical results are illustrated via the application to a reactor–separator chemical process.     

Cooperative control with distributed gain adaptation and connectivity estimation for directed networks

This paper addresses the problem of how to achieve superior performance by adaptively and distributively adjusting control gains of a cooperative control system. It is shown that according to distributed observations of changing network topologies and on the basis of online estimation of network connectivity, cooperative controls with adaptive gains can be synthesized to making the time derivative of the cooperative control Lyapunov function more negative and hence to improve stability and convergence of the overall system. For undirected networks, the proposed adaptive design reduces to improving the Fiedler eigenvalue (algebraic connectivity) as well as other eigenvalues. On the other hand, connectivity of a directed network is characterized by the property of the first left eigenvector(s) associated with its dominant eigenvalue, and in this paper, a distributed high‐gain observer design is proposed for each of the networked systems to utilize the same communication network among the systems. It is shown that even in the presence of transmission delays, the distributed estimators converge fast to the first left eigenvector(s) of the network. In addition, the expected consensus value(s) of the overall cooperative system under control is also estimated in a distributive manner. Rigorous analysis is carried out on estimation convergence and observer gain selection. It is shown that the proposed estimation and adaptive control designs are fully distributed, have guaranteed performance for all possible varying topologies as long as their dwelling times are bounded away from zero, and are robust with respect to excessively fast topology changes. Simulation results are included to demonstrate effectiveness of the proposed estimation and control schemes. 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.     

Optimal sequential and distributed fusion for state estimation in cross-correlated noise

This paper is concerned with the optimal state estimation for linear systems when the noises of different sensors are cross-correlated and also coupled with the system noise of the previous step. We derive the optimal linear estimation in a sequential form and for distributed fusion. They are both compared with the optimal batch fusion, suboptimal batch fusion, suboptimal sequential fusion, and the suboptimal distributed fusion where the cross-correlation between the noises are neglected. The comparison is in terms of theoretical filter mean square error and the real root mean square error. Simulation on a target tracking example is given to show the effectiveness of the presented algorithms.     

Event-triggered robust distributed state estimation for sensor networks with state-dependent noises

This paper is concerned with the event-triggered distributed state estimation problem for a class of uncertain stochastic systems with state-dependent noises and randomly occurring uncertainties over sensor networks. An event-triggered communication scheme is proposed in order to determine whether the measurements on each sensor should be transmitted to the estimators or not. The norm-bounded uncertainty enters into the system in a random way. Through available output measurements from not only the individual sensor but also its neighbouring sensors, a sufficient condition is established for the desired distributed estimator to ensure that the estimation error dynamics are exponentially mean-square stable. These conditions are characterized in terms of the feasibility of a set of linear matrix inequalities, and then the explicit expression is given for the distributed estimator gains. Finally, a simulation example is provided to show the effectiveness of the proposed event-triggered distributed state estimation scheme.     

Cooperative state estimation of multi-agent systems subject to bounded external disturbances

This paper deals with the problem of cooperative state estimation of general linear multi-agent systems subject to heterogeneous bounded external disturbances. This problem specifies the objective that each agent estimates its own state by using only relative information from its neighbours. Because of the existence of external disturbances, the problem is challenging especially when stringent exact estimation performance is desired. To this end, two cooperative estimation protocols are proposed, including the discontinuous nonlinear protocol for exact state estimation and the continuous nonlinear protocol for estimation with bounded errors. The overall network stability and convergence properties are analysed using the Lyapunov function method. A simulation example has also been used to demonstrate the effectiveness of the proposed results.     

Stubborn state estimation for nonlinear distributed parameter systems subject to measurement outliers

In this article, the state estimation problem is investigated for a class of distributed parameter systems (DPSs). In order to estimate the state of DPSs, we give a partition of spatial interval with a finite sequence and, on each subinterval, one sensor is placed to receive the measurements from the DPS. Due to the unexpected environment changes, the measurements will probably contain some outliers. To eliminate the effects of the possibly occurring outliers, we construct a stubborn state estimator where the innovation is constrained by a saturation function. By using Lyapunov functional, Wirtinger inequality and piecewise integration, some sufficient conditions are obtained under which the resulting estimation error system is exponentially stable and the performance requirement is satisfied. According to the obtained analysis results, the desired state estimator is designed in terms of the solution to a set of matrix inequalities. Finally, a numerical simulation example is given to verify the effectiveness of the proposed state estimation scheme.     

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.     

Real time distributed parameter state estimation applied to a two dimensional heated ingot

A distributed parameter state estimator, implemented via a minicomputer, was used to estimate the radial and axial temperature distribution of a stainless steel cylindrical ingot being heated in a three zone furnace. The filter estimates as well as the estimate covariances were calculated by reduction of the distributed equations to ordinary differential equations via modal decomposition. The filter was shown to be robust and rapidly convergent even in cases of high measurement noise, few sensors, and poor initial conditions. The on line computations were accomplished in less than half of real-time. Since typical industrial applications involve time constants which are two orders of magnitude larger than for this laboratory system, the feasibility of such estimation algorithms in a multiprocess industrial environment seems assured.     

Event-triggered zero-gradient-sum distributed convex optimisation over networks with time-varying topologies

This paper focuses on a distributed convex optimisation problem over networks with time-varying topologies. First, an event-triggered strategy is employed to reduce computation and communication load in the networked systems. Second, the exponential convergence of event-triggered zero-gradient-sum algorithm is guaranteed if the corresponding time-varying network topology satisfies a new connected condition, called cooperatively connected condition. This condition does not require topologies constantly connected or jointly connected but only requires the integral of the Laplacian matrix of the network topology over a period of time is connected. Hence, it is suitable for more general time-varying topologies. Third, a convergence analysis technique is developed which is based on the difference of the Lyapunov function rather than its differentiation. Finally, a simulation example is provided to verify the results obtained in this paper.     

Media hash-dependent image watermarking resilient against both geometric attacks and estimation attacks based on false positive-oriented detection

The major disadvantage of existing watermarking methods is their limited resistance to extensive geometric attacks. In addition, we have found that the weakness of multiple watermark embedding methods that were initially designed to resist geometric attacks is their inability to withstand the watermark-estimation attacks (WEAs), leading to reduce resistance to geometric attacks. In view of these facts, this paper proposes a robust image watermarking scheme that can withstand geometric distortions and WEAs simultaneously. Our scheme is mainly composed of three components: 1) robust mesh generation and mesh-based watermarking to resist geometric distortions; 2) construction of media hash-based content-dependent watermark to resist WEAs; and 3) a mechanism of false positive-oriented watermark detection, which can be used to determine the existence of a watermark so as to achieve a tradeoff between correct detection and false detection. Furthermore, extensive experimental results obtained using the standard benchmark (i.e., Stirmark) and WEAs, and comparisons with relevant watermarking methods confirm the excellent performance of our method in improving robustness. To our knowledge, such a thorough evaluation has not been reported in the literature before.     

Damage assessment and repair in attack resilient distributed database systems

Preventive measures sometimes fail to defect malicious attacks. With attacks on data-intensive applications becoming an ever more serious threat, intrusion tolerant database systems are a significant concern. The main objective of such systems is to detect attacks, and to assess and repair the damage in a timely manner. This paper focuses on efficient damage assessment and repair in distributed database systems. The complexity caused by data partition, distributed transaction processing, and failures makes intrusion recovery much more challenging than in centralized database systems. This paper identifies the key challenges and presents an efficient algorithm for distributed damage assessment and repair.     

Decentralized state observers for range‐based position and velocity estimation in acyclic formations with fixed topologies

This paper addresses the problem of decentralized position and velocity estimation in formations of autonomous vehicles. A limited number of vehicles in the formation have access to absolute position measurements, while the rest must rely on range measurements to neighboring agents, local sensor data, and limited communication capabilities to estimate their own position and velocity. The contribution is threefold: (i) a method for designing local state observers for each agent in the formation that rely only on locally available information is presented; (ii) the stability of the continuous‐time linear time‐varying Kalman filter subject to exponentially decaying perturbations in some variables is studied; and (iii) the stability of the error dynamics of the resulting decentralized state observer is analyzed for acyclic formations with fixed topologies, and it is shown that the error converges exponentially fast to the origin for all initial conditions. Simulation results are presented and discussed to validate the proposed solution, as well as assessing its performance under the influence of measurement noise. Copyright © 2015 John Wiley & Sons, Ltd.