Secure State Estimation Problem Research Articles

Secure state estimation for affine T-S fuzzy systems under sparse sensor attacks

This paper is concerned with the secure state estimation problem of affine T-S fuzzy systems under sparse sensor attacks. The objective is to construct a bank of fuzzy state estimators with an adaptive switching mechanism to ensure the attacked sensor measurements be isolated, and the estimation error system is asymptotic stable with a guaranteed H∞ performance. The case of unmeasurable plant premise variables is considered, which leads to the estimator implementation according to estimators’ state-space partitions may not be always synchronous with the plant. By constructing piecewise Lyapunov functions and employing the S-procedure and matrices decoupled techniques, the constructed state estimators synthesis conditions are derived in linear matrix inequalities (LMIs) form. Compared with existing methods, the proposed approach avoids restrictions on the structure of Lyapunov matrices and derives less conservative estimator design conditions. Finally, the effectiveness and superiorities of the proposed method is verified with a numerical example.

Trust-Based Distributed Secure State Estimation Against Malicious Agents via Two-Hop Communication

This paper studies the distributed secure state estimation problem in unreliable multiagent networks through adversary detection. The agents are endowed with the capacity for detecting malicious neighbors and aim to collaboratively estimate the state variables of a dynamic system in the presence of malicious agents. A trust mechanism is first introduced to characterize the reliability of the information received from in-neighbors and identify the reliable information of two-hop in-neighbors. With the help of the trust mechanism and two-hop communication, two distributed secure state estimation schemes with adversary detection algorithms are developed under different resource requirements and adversary models. Necessary and sufficient conditions on the graph connectivity and joint detectability are established to guarantee that all the regular agents can detect the malicious in-neighbors and generate accurate estimates. An example is given to show the effectiveness of the proposed methods.

Secure State Estimation for Artificial Neural Networks With Unknown-But-Bounded Noises: A Homomorphic Encryption Scheme.

This article is concerned with the secure state estimation problem for artificial neural networks (ANNs) subject to unknown-but-bounded noises, where sensors and the remote estimator are connected via open and bandwidth-limited communication networks. Using the encoding-decoding mechanism (EDM) and the Paillier encryption technique, a novel homomorphic encryption scheme (HES) is introduced, which aims to ensure the secure transmission of measurement information within communication networks that are constrained by bandwidth. Under this encoding-decoding-based HES, the data being transmitted can be encrypted into ciphertexts comprising finite bits. The emphasis of this research is placed on the development of a secure set-membership state estimation algorithm, which allows for the computation of estimates using encrypted data without the need for decryption, thereby ensuring data security throughout the entire estimation process. Taking into account the unknown-but-bounded noises, the underlying ANN, and the adopted HES, sufficient conditions are determined for the existence of the desired ellipsoidal set. The related secure state estimator gains are then derived by addressing optimization problems using the Lagrange multiplier method. Lastly, an example is presented to verify the effectiveness of the proposed secure state estimation approach.

A Polynomial-Time Algorithm for the Secure State Estimation Problem Under Sparse Sensor Attacks via State Decomposition Technique

This paper investigates the secure state estimation problem for cyber-physical systems (CPSs) under sparse sensor attacks. In the existing results, the secure state estimation is usually established as an NP-hard problem where combinatorial candidates should be checked since the set of attacked channels is unknown. For avoiding brute force search, a novel state decomposition technique is proposed such that the state can be reconstructed by a simple majority vote. Necessary and sufficient conditions for the observability of the decomposition elements are given, and based on the obtained conditions, an effective algorithm for designing the decomposition matrix is also proposed. Then, a polynomial-time secure state estimation strategy is constructed based on the proposed state decomposition technique. It is shown that besides <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\text{2}~s$</tex-math></inline-formula> -sparse eigenvalue observable systems, the secure state estimation problem can be solved in polynomial time for more general cases where each decomposition element is <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\mathbb {B}$</tex-math></inline-formula> -observable for at least <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$2s+1$</tex-math></inline-formula> sensors. Finally, the effectiveness of the proposed methods is demonstrated by two simulations showing the decrease of computational complexity and the effectiveness under different cases.

Encryption-Decryption-Based State Estimation With Multirate Measurements Against Eavesdroppers: A Recursive Minimum-Variance Approach

This paper is concerned with the secure state estimation problem for a networked system with multi-rate measurements. The measurement data are transmitted to the estimator over a communication network, where an eavesdropper could intercept the transmitted information and generate the state estimates based on the overheard signals. In order to protect the privacy of the system state from information leakage, a novel encryptor is proposed to encrypt the measurement signals into codewords before being transmitted, and a decryptor is then adopted at the user side to decrypt the received codewords into the desired measurement signals, based on which a recursive state estimator is developed whose parameter is calculated by solving several coupled difference equations. Here, the secret key for decryption is available to the user but is unknown to the eavesdropper. The encryptor and the estimator are co-designed such that 1) at the user side, the estimation error covariance has an upper bound that is subsequently minimized in the sense of the matrix trace, where the uniform boundedness of the error covariance is also examined; and 2) at the eavesdropper side, the corresponding state estimation error is divergent. Two simulation examples are provided to demonstrate the effectiveness of our developed secure state estimation scheme.

Secure State Estimation Under Sparse Sensor Attacks Via Saturating Adaptive Technique

This paper is concerned with the secure state estimation problem of cyber-physical systems (CPSs) in the presence of sparse sensor attacks. Considering that such problem is a combinatorial problem in nature, novel saturating adaptive algorithms are proposed to reconstruct the system state from the corrupted measurements. Through introducing saturating adaptive terms limiting the impact of attacks, state estimates are obtained without brute force search and the computational complexity is reduced greatly. Meanwhile, it is shown that the proposed method also can be adopted to estimate the system state under the attacks with varying attack targets. Finally, simulation results are provided to illustrate the effectiveness of the proposed methods.

Secure state estimation and actuator attack reconstruction for cyber‐physical systems based on sliding‐mode observer

AbstractIn this paper, the secure state estimation attack and reconstruction problems are considered for linear cyber‐physical systems (CPSs) under actuator attacks and unknown disturbances. By introducing a continuous sliding mode observer with an exponential reaching law strategy, the dynamic quality of approach motion is greatly improved and the chattering is eliminated. Then by transforming the original system into a special attack channel separation form so that an improved sliding mode observer with disturbance compensation is obtained to solve the secure state estimation problem. In addition, with the obtained observer's information, not only the actuator attack can be reconstructed but also the estimation of the disturbance can be obtained. Meanwhile, the influence of disturbance estimation error on attack reconstruction can be attenuated. Finally, simulations on a VTOL aircraft are presented to verify the effectiveness of the proposed scheme.

Secure state estimation for complex networks with multi-channel oriented round robin protocol

This paper focuses on the secure state estimation problem for complex networks (CNs) which are compromised by deception attack and constrained with limited communication resource. Firstly, a multi-channel oriented round robin (RR) protocol is proposed to schedule the data transferred over the communication network consisting of multiple transmission channels. The extended RR protocol can not only avoid the data collision caused by limited communication resource, but also fully utilize the sliced network bandwidth. Then, a state estimation error model is constructed by further considering the influence of deception attack. Following the model, efficient state estimators are designed based on analyzing the sufficient conditions that assuring the stability of the formulated state estimation error system. Finally, numerical results are presented to validate the theoretical outcomes.

Distributed secure state estimation for linear systems against malicious agents through sorting and filtering

This paper investigates the distributed secure state estimation problem for the cyber–physical systems monitored by a multi-agent network where partial agents are malicious. Through introducing a sort and filter approach, a novel distributed secure state estimation strategy, where the impact of malicious agents is mitigated through discarding partial extreme values from the received vectors, is proposed. Sufficient conditions on the graph topology and the system matrices to tolerant a bounded number of malicious agents are given. It is shown that by adopting the proposed secure state estimation strategy, normal agents can effectively generate correct state estimate in the presence of malicious agents. Besides, for efficiently updating the state estimate while new measurements are available, a distributed observer is also designed. Compared with the existing techniques searching an appropriate candidate from multiple ones, the proposed secure state estimation strategies are much more computationally efficient since reliable state estimates are generated without brute force search. Finally, simulation results are provided to illustrate the effectiveness of the proposed algorithms.

A transmission scheme for secure estimation of cyber-physical systems against malicious attack

This paper investigates the secure state estimation problem of the cyber-physical systems (CPSs) in the presence of malicious attacks. Considering the destructiveness and stealthiness of the attacker, a novel stochastic transmission scheme, in which the repeater generates transmission data by randomly combining some measurement values, is proposed to ensure the effectiveness of the attack detector. A filter equipped with the χ 2 detector and the stochastic transmission scheme is proposed to conduct the secure state estimation. The attack probability condition of the estimation error being mean-square bounded is given, which indicates that stochastic transmission scheme has a limited effect on the filter. Some numerical simulations are given to illustrate the effectiveness of the proposed transmission scheme.

False Data Injection Attack for Switched Systems

This paper studies the secure state estimation problem for switched systems. The single/joint false data injection attacks are designed with the aim at altering the sensor signal and/or switching signal. Firstly, it is shown that the attack will steer system state to infinity but could be detectable by χ2 detector when only the switching signal is attacked. In addition, the attack acting on sensor signal is designed, which can be recognized by the summation (SUM) detector but fails by χ2 detector. Then a joint attack strategy is devised and a sufficient condition is given to guarantee that the joint attack is strictly stealthy. The joint attack performs well since it can launch a strictly stealthy attack compared with the sensor signal attack. Finally, a numerical example is given to verify the theoretical results.

Disturbance decoupled secure state estimation: An orthogonal projection-based method

This paper investigates the disturbance decoupled secure state estimation problem of a linear system in the presence of sparse sensor attacks and unknown disturbances, where disturbance decoupled state estimation means that the resulting estimate errors do not depend on the value of disturbances. First, the solvability of the disturbance decoupled secure state estimation problems is analyzed by introducing the concepts of redundantly strong observability and redundantly strong detectability. It is proved that the states can be reconstructed (estimated asymptotically) despite the existence of attacks and disturbances if and only if the system is redundantly strongly observable (redundantly strongly detectable). Second, the design procedure for reconstructing (asymptotically estimating) the states is provided based on the orthogonal projection technique. Specifically, by calculating a sequence of orthogonal projections of the sensors’ measurements, a residual signal is constructed to identify a reliable set for state reconstruction (asymptotic state estimation), and then a least square-based method (an observer-based method) is proposed to reconstruct (asymptotically estimate) the states. Third, the effects of numerical errors on the residual signals are discussed. Finally, two examples are given to validate the effectiveness of the proposed methods.

Finite‐time secure state estimation for a class of switched systems subject to deception attacks

AbstractThis article is concerned with the finite‐time secure state estimation problem for switched systems subject to malicious attacks. The sensor data is considered transmissible via a non‐secure communication network environment, where the communication channel might be subject to deception attacks. By dividing the sensor data that is subject to attacks into two parts, related and unrelated to the original measurements, a switched secure state estimation error system model is established. Moreover, based on the average dwell time method, sufficient conditions are derived for the switched secure state estimation error system to be finite‐time stable, as well as finite‐time boundedness. An existence condition of the finite‐time secure state estimator gains with a desired performance is given. Subsequently, the finite‐time secure state estimator gains' design is transformed to solve a set of linear matrix inequalities. Finally, numerical examples are used in order to show the effectiveness of the proposed finite‐time secure state estimator design method.

Secure State Estimation With Switched Compensation Mechanism Against DoS Attacks.

This article is concerned with the secure state estimation problem for cyber-physical systems under intermittent denial-of-service (DoS) attacks. Based on a switching scheme and the cascade observer technique, a novel resilient state observer with a switched compensation mechanism is designed. Moreover, a quantitative relationship between the resilience against DoS attacks and the design parameters is revealed. Compared with the existing results, where only the boundedness of the estimation error is guaranteed under DoS attacks, the exponential convergence of the estimation error is achieved by employing the proposed observer scheme, such that the estimation performance is improved. More specifically, in the disturbance-free case, it is proven that the state estimation error converges exponentially to 0 despite the existence of DoS attacks. Finally, simulation results are provided to illustrate the effectiveness and merits of the proposed methods.

Probability-Guaranteed Distributed Secure Estimation for Nonlinear Systems Over Sensor Networks Under Deception Attacks on Innovations

This paper studies the distributed secure state estimation problem for a class of general nonlinear systems over sensor networks under unknown deception attacks on innovations. At each sensing node, an estimator is designed to generate the state estimate by making use of the local measurements in combination with the neighbours’ information shared via the communication network. During the transmission of innovations among nodes, the data are maliciously falsified by adversaries in a random way. A neural-network-based mechanism is put forward to approximate the unknown falsified innovations with the aim to mitigate the effects on the estimation performance. The objective of the addressed problem is to develop a distributed estimation approach to jointly estimate the system states as well as the unknow deception attacks, ensuring that the state estimation errors at each sensing node reside within required ellipsoidal regions with a pre-specified probability. With the help of certain convex optimization methods, we obtain sufficient conditions for the solvability of the addressed problem and the desired estimator gains can be iteratively computed by solving a series of matrix inequalities. On basis of the proposed framework, some optimization problems are presented to determine sub-optimal estimator parameters from different perspectives. Finally, the applicability of the developed algorithms is validated via a numerical simulation example.

Local Decomposition of Kalman Filters and its Application for Secure State Estimation

This article is concerned with the secure state estimation problem of a linear discrete-time Gaussian system in the presence of sparse integrity attacks. <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\mathbf {m}$</tex-math></inline-formula> sensors are deployed to monitor the state and <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\mathbf {p}$</tex-math></inline-formula> of them can potentially be compromised by an adversary, whose data can be arbitrarily manipulated by the attacker. We show that the optimal Kalman estimate can be decomposed as a weighted sum of local state estimates. Based on these local estimates, we propose a convex optimization based approach to generate a more secure state estimate. It is proved that our proposed estimator coincides with the Kalman estimator with a certain probability when all sensors are benign. Besides, we establish a sufficient condition under which the proposed estimator is stable against the <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\mathbf {(p,m)}$</tex-math></inline-formula> -sparse attack. A numerical example is provided to validate the secure state estimation scheme.

Distributed Secure State Estimation in the Presence of Malicious Agents

This article investigates the distributed secure state estimation problem of distributed systems where a set of agents estimates the state cooperatively in the presence of malicious agents. First, a sufficient condition for the solvability of the distributed secure state estimation problem is proposed. Second, based on the obtained condition, a distributed switched gradient descent (DSGD) algorithm is designed to solve the considered problem which is transformed into a distributed optimization problem. With the help of a candidate-removal mechanism, the proposed DSGD algorithm successfully generates reliable state estimates despite malicious agents. Finally, the effectiveness of the proposed algorithm is illustrated by a numerical example.

Secure State Estimation for Motion Monitoring of Intelligent Connected Vehicle Systems.

This paper considers the state estimation problem of intelligent connected vehicle systems under the false data injection attack in wireless monitoring networks. We propose a new secure state estimation method to reconstruct the motion states of the connected vehicles equipped with cooperative adaptive cruise control (CACC) systems. First, the set of CACC models combined with Proportion-Differentiation (PD) controllers are used to represent the longitudinal dynamics of the intelligent connected vehicle systems. Then the notion of sparseness is employed to model the false data injection attack of the wireless networks of the monitoring platform. According to the corrupted data of the vehicles’ states, the compressed sensing principle is used to describe the secure state estimation problem of the connected vehicles. Moreover, the L1 norm optimization problem is solved to reconstruct the motion states of the vehicles based on the orthogonaldecomposition. Finally, the simulation experiments verify that the proposed method can effectively reconstruct the motion states of vehicles for remote monitoring of the intelligent connected vehicle system.

Secure State Estimation for Multiagent Systems With Faulty and Malicious Agents

This paper investigates the secure state estimation problem of multiagent systems with misbehaving agents. Compared with the existing works which only consider malicious behaviors generated elaborately, a class of faulty behaviors generated randomly is also taken into account. By assuming that faulty behaviors cannot be altered by the adversaries, the notion of orthogonal complement matrix is introduced to characterize the state observability of the multiagent systems with both faulty and malicious agents. It is shown that more misbehaving agents can be tolerated by distinguishing faulty agents from malicious ones. Then, for single agent, two algorithms are provided to estimate the state based on its own value and the measurements obtained from its neighbors. Finally, two simulations are provided to illustrate the correctness and effectiveness of the proposed conditions and methods.

Switched projected gradient descent algorithms for secure state estimation under sparse sensor attacks

This paper investigates the secure state estimation problem of cyber–physical systems (CPSs) under sparse sensor attacks. First, a novel algorithm, which uses a switched gradient descent technique to harness the intrinsic combinatorial complexity of the secure state estimation problem, is proposed to estimate the state. The computational complexity is reduced through improving the convergence rate, reducing the number of candidates to be searched, reducing the search times, and reducing the computing resources consumed by each incorrect candidate selection simultaneously. Second, based on the proposed switched gradient descent algorithm, an observer-based algorithm is proposed to efficiently update the state estimation while new measurements are available. Compared with the existing methods, the computational complexity is reduced greatly without introducing any constraint except the basic observability assumption by adopting the proposed algorithms.