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.     

Stealthy switching attacks on sensors against state estimation in cyber-physical systems

This article focuses on designing sensor attacks to deteriorate the state estimation in cyber-physical systems. The scenario that the malicious attack signals can be injected into different but limited number of sensor communication channels is considered. The state estimation error variations and innovation variations are adopted to measure attack performance and attack stealthiness, respectively. A switching attack strategy is proposed, under which the estimation error variations are driven to the predesigned target value and the norm of innovation variations remains at a small level. The switching attack design problem is formulated as a discrete switched optimal control problem which can be solved by dynamic programming, while the computational burden is heavy. To overcome this difficulty, by using pruning technique to remove the redundant matrices generated in dynamic programming, the quadratic optimization problem becomes numerically tractable. In this way, the suboptimal attack signal sequence and switching sequence can be acquired. Finally, a simulation example is provided to illustrate the effectiveness of the proposed attack strategy.     

Reconstruction of measurements in state estimation strategy against deception attacks for cyber physical systems

Without the known state equation, a new state estimation strategy is designed to be against malicious attacks for cyber physical systems. Inspired by the idea of data reconstruction, the compressive sensing (CS) is applied to reconstruction of residual measurements after the detection and identification scheme based on the Markov graph of the system state, which increases the resilience of state estimation strategy against deception attacks. First, the observability analysis is introduced to decide the triggering time of the measurement reconstruction and the damage level from attacks. In particular, the dictionary learning is proposed to form the over completed dictionary by K singular value decomposition (K SVD), which is produced adaptively according to the characteristics of the measurement data. In addition, due to the irregularity of residual measurements, a sampling matrix is designed as the measurement matrix. Finally, the simulation experiments are performed on 6 bus power system. Results show that the reconstruction of measurements is completed well by the proposed reconstruction method, and the corresponding effects are better than reconstruction scheme based on the joint dictionary and the traditional Gauss or Bernoulli random matrix respectively. Especially, when only 29% available clean measurements are left, performance of the proposed strategy is still extraordinary, which reflects generality for five kinds of recovery algorithms.     

Distributed moving horizon state estimation for nonlinear systems with bounded uncertainties

In this work, we propose a distributed moving horizon state estimation (DMHE) design for a class of nonlinear systems with bounded output measurement noise and process disturbances. Specifically, we consider a class of nonlinear systems that are composed of several subsystems and the subsystems interact with each other via their subsystem states. First, a distributed estimation algorithm is designed which specifies the information exchange protocol between the subsystems and the implementation strategy of the DMHE. Subsequently, a local moving horizon estimation (MHE) scheme is designed for each subsystem. In the design of each subsystem MHE, an auxiliary nonlinear deterministic observer that can asymptotically track the corresponding nominal subsystem state when the subsystem interactions are absent is taken advantage of. For each subsystem, the nonlinear deterministic observer together with an error correction term is used to calculate a confidence region for the subsystem state every sampling time. Within the confidence region, the subsystem MHE is allowed to optimize its estimate. The proposed DMHE scheme is proved to give bounded estimation errors. It is also possible to tune the convergence rate of the state estimate given by the DMHE to the actual system state. The performance of the proposed DMHE is illustrated via the application to a reactor-separator process example.     

网络攻击下的信息物理系统安全状态估计研究综述

近年来,信息物理系统在工业界的广泛应用引起了人们对系统安全问题的极大关注.信息物理系统对通信网络的深度依赖,使得网络攻击成为其中最为严峻的威胁之一,特别是那些能够干扰系统状态认知的攻击,因此,安全状态估计(即在遭受攻击时正确估计系统状态)已成为各界广泛关注的安全问题之一.此文旨在总结网络攻击下信息物理系统安全状态估计研究的进展.首先,介绍典型的网络攻击,并详细阐述在稀疏攻击下的安全状态估计问题.其次,探讨集中式安全状态估计和分布式安全状态估计的研究现状.在考虑稀疏攻击下安全状态估计问题的难点时,关键在于如何快速找到受到攻击的信道集合(这可能涉及到高计算复杂度).因此,将安全状态估计方法分为遍历搜索和非遍历搜索两大类,并对现有方法的优缺点进行归纳总结和详细阐述.然后,介绍稀疏攻击下信息物理系统安全状态能观性分析的研究现状.现有的研究结果表明:增加检测机制或先验知识可以缓解在稀疏攻击下安全状态估计所需的基础冗余度要求;同时,通过区分攻击和故障,也能有效降低传感器冗余度要求.最后,对信息物理系统安全状态估计仍然存在的问题进行展望,并提出一些可能的解决方向.     

Noise modeling concepts in nonlinear state estimation

It is quite common to assume that uncertainty enters through additive white noise sources when using recursive state estimation algorithms. Also unknown and time-varying parameters are often modeled similarly by augmenting the states with a parameter vector. Further, it is common to reflect initial model uncertainty through the choice of the initial covariance matrices for the states and parameters.In this paper we study noise modeling based on a hypothesis that it is important to model noise correctly. In practice this implies a critical view on the dominating ‘additive noise paradigm’ as a means to model uncertainty. Alternative concepts of modeling the noise are investigated, and it is shown that modeling noise by introducing it in the system auxiliary variables and control inputs may have a positive impact on estimation performance.     

Active state estimation of nonlinear systems

In this paper, state observers for control systems with nonlinear outputs are studied. For such systems, the observability does not only depend on the initial conditions, but also on the exciting control used. Thus, for such systems, design of active control is an integral part of the design for state observers. Here some sufficient conditions are given for the convergence of an observer. It is also discussed, via a camera example, how to actively excite a system in order to improve the observability.     

网络攻击下一类非线性切换多智能体系统的安全自适应控制

针对一类控制方向未知的非线性切换多智能体系统, 本文研究了在不确定网络攻击下的安全控制问题. 网 络攻击破坏传感器真实数据, 导致系统真实信息无法获取且不能直接用于控制设计. 为此, 通过受攻击状态构建一 组新颖辅助变量来消除网络攻击造成的影响. 此外, 所研究的系统包含更一般的不确定性, 即未知控制方向, 未知常 值参数以及不确定攻击. 这些不确定性在设计过程中相互耦合. 利用Nussbaum型函数并设计自适应律补偿耦合后 的不确定性, 极大降低了系统复杂性. 通过系统性地迭代构造出共同Lyapunov函数, 提出了一套安全自适应控制方 法, 保证了受攻击系统在任意切换下达到渐近输出一致性. 最后, 数值仿真验证了该方法的有效性.     

Neural networks for nonlinear state estimation

Estimating the state of a nonlinear stochastic system (observed through a nonlinear noisy measurement channel) has been the goal of considerable research to solve both filtering and control problems. In this paper, an original approach to the solution of the optimal state estimation problem by means of neural networks is proposed, which consists in constraining the state estimator to take on the structure of a multilayer feedforward network. Both non-recursive and recursive estimation schemes are considered, which enable one to reduce the original functional problem to a nonlinear programming one. As this reduction entails approximations for the optimal estimation strategy, quantitative results on the accuracy of such approximations are reported. Simulation results confirm the effectiveness of the proposed method.     

Set membership state and parameter estimation for systems described by nonlinear differential equations

This paper investigates the use of guaranteed methods to perform state and parameter estimation for nonlinear continuous-time systems, in a bounded-error context. A state estimator based on a prediction-correction approach is given, where the prediction step consists in a validated integration of an initial value problem for an ordinary differential equation (IVP for ODE) using interval analysis and high-order Taylor models, while the correction step uses a set inversion technique. The state estimator is extended to solve the parameter estimation problem. An illustrative example is presented for each part.     

Applying the unscented Kalman filter for nonlinear state estimation

Based on presentation of the principles of the EKF and UKF for state estimation, we discuss the differences of the two approaches. Four rather different simulation cases are considered to compare the performance. A simple procedure to include state constraints in the UKF is proposed and tested. The overall impression is that the performance of the UKF is better than the EKF in terms of robustness and speed of convergence. The computational load in applying the UKF is comparable to the EKF.     

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.     

Comments on: “Exact and approximate state estimation for nonlinear dynamic systems”

After deriving the realizable, nonlinear filtering algorithm for dynamic systems involving white and non-white processes, the above paper (Liang and Christensen, 1975) extended the algorithm to dynamic systems having noise-free observation. However, the resulted nonlinear noise-free filtering is not correct since the paper overlooked the Itô stochastic calculus to differentiate noise-free nonlinear measurements. Here we show the correct extension.     

A separated bias identification and state estimation algorithm for nonlinear systems

A computational algorithm for the identification of biases in discrete-time, nonlinear, stochastic systems is derived by extending the separate bias estimation results for linear systems to the extended Kalman filter formulation. The merits of the approach are illustrated by identifying instrument biases using a terminal configured vehicle simulation.     

Joint state and parameter robust estimation of stochastic nonlinear systems

Successful implementation of many control strategies is mainly based on accurate knowledge of the system and its parameters. Besides the stochastic nature of the systems, nonlinearity is one more feature that may be found in almost all physical systems. The application of extended Kalman filter for the joint state and parameter estimation of stochastic nonlinear systems is well known and widely spread. It is a known fact that in measurements, there are inconsistent observations with the largest part of population of observations (outliers). The presence of outliers can significantly reduce the efficiency of linear estimation algorithms derived on the assumptions that observations have Gaussian distributions. Hence, synthesis of robust algorithms is very important. Because of increased practical value in robust filtering as well as the rate of convergence, the modified extended Masreliez–Martin filter presents the natural frame for realization of the joint state and parameter estimator of nonlinear stochastic systems. The strong consistency is proved using the methodology of an associated ODE system. The behaviour of the new approach to joint estimation of states and unknown parameters of nonlinear systems in the case when measurements have non‐Gaussian distributions is illustrated by intensive simulations. Copyright © 2015 John Wiley & Sons, Ltd.     

Simultaneous input and state estimation for nonlinear systems with applications to flow field estimation

This paper studies the problem of simultaneous input and state estimation (SISE) for nonlinear dynamical systems with and without direct input–output feedthrough. We take a Bayesian perspective to develop a sequential joint input and state estimation approach. Our scheme gives rise to a nonlinear Maximum a Posteriori optimization problem, which we solve using the classical Gauss–Newton method. The proposed approach generalizes a number of SISE methods presented in the literature. We illustrate the effectiveness of the proposed scheme for nonlinear systems with direct feedthrough in an oceanographic flow field estimation problem involving submersible drogues that measure position intermittently and acceleration continuously.     

Fixed‐time state estimation for a class of switched nonlinear time‐varying systems

This paper deals with the state estimation problem of a class of nonlinear time‐varying systems with switched dynamics. Based on the concept of fixed‐time stability, an observer is designed to reconstruct the continuous state of switched nonlinear time‐varying systems with state jumps, satisfying the minimal dwell‐time condition. Using the past input and output values of the studied system, some sufficient conditions are provided to estimate the state before the next switching. Some numerical results illustrate the effectiveness of the proposed scheme.     

A bounded-error approach to simultaneous state and actuator fault estimation for a class of nonlinear systems

This paper proposes an approach for the joint state and fault estimation for a class of uncertain nonlinear systems with simultaneous unknown input and actuator faults. This is achieved by designing an unknown input observer combined with a set-membership estimation in the presence of disturbances and measurement noise. The observer is designed using quadratic boundedness approach that is used to overbound the estimation error. Sufficient conditions for the existence and stability of the proposed state and actuator fault estimator are expressed in the form of linear matrix inequalities (LMIs). Simulation results for a quadruple-tank system show the effectiveness of the proposed approach.     

Extended state observer for uncertain lower triangular nonlinear systems

The extended state observer (ESO) is a key part of the active disturbance rejection control approach, a new control strategy in dealing with large uncertainty. In this paper, a nonlinear ESO is designed for a kind of lower triangular nonlinear systems with large uncertainty. The uncertainty may come from unmodeled system dynamics and external disturbance. We first investigate a nonlinear ESO with high constant gain and present a practical convergence. Two types of ESO are constructed with explicit error estimations. Secondly, a time varying gain ESO is proposed for reducing peaking value near the initial time caused by constant high gain approach. The numerical simulations are presented to show visually the peaking value reduction. The mechanism of peaking value reduction by time varying gain approach is analyzed.