Secure State Research Articles

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.

Marine ecological security assessment from the perspective of emergy ecological footprint

IntroductionMarine ecological security assessments are considered as a basis for coordinating marine economic development and ecological protection.MethodsWe propose an assessment method based on the emergy ecological footprint which first measures the emergy of the natural and economic elements of the marine ecosystem. Considering the role of economic, social and waste discharge factors in the marine ecosystem, an ecological security evaluation index is constructed, and a dynamic evaluation is conducted based on long time series data to characterize the change trend of ecological security.ResultsThe Guangxi marine ecosystem was selected as the case study, and the ecological security dynamic evaluation was conducted by collecting data from 2008 to 2020. The results show that Guangxi's marine ecosystem has always been in an ecologically secure state, but since 2010, the emergy ecological footprint intensity has been increasing, indicating ecosystem deterioration. Therefore, some targeted suggestions are put forward.DiscussionThis method provides a new assessment tool for marine ecological security evaluation and offers guidance for the sustainable development and utilization of marine ecosystems.

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.

Secure State Estimation against Sparse Attacks on a Time-varying Set of Sensors

This paper studies the problem of secure state estimation of a linear time-invariant (LTI) system with bounded noise in the presence of sparse attacks on an unknown, time-varying set of sensors. At each time, the attacker has the freedom to choose an arbitrary set of no more than p sensors and manipulate their measurements without restraint. To this end, we propose a secure state estimation scheme and guarantee a bounded estimation error irrespective of the attack signals subject to 2p-sparse observability and a mild, technical assumption that the system matrix has no degenerate eigenvalues. The proposed scheme comprises a design of decentralized observers for each sensor based on the local observable subspace decomposition. At each time step, the local estimates of sensors are fused by a median operator to obtain a secure estimation, which is then followed by a local detection-and-resetting process of the decentralized observers. The estimation error is shown to be upper-bounded by a constant which is determined only by the system parameters and noise magnitudes. Moreover, we design the detector threshold to ensure that the benign sensors never trigger the detector. The efficacy of the proposed algorithm is demonstrated by its application on a benchmark example of IEEE 14-bus system. We show that our proposed scheme can effectively tolerate sparse attacks on an unknown set of sensors, ensuring a bounded estimation error and effectively detecting and resetting the attacked sensors.

Distributed Secure State Estimation of Multi-Agent Systems Under Homologous Sensor Attacks

This paper addresses the problem of distributed secure state estimation for multi-agent systems under homologous sensor attacks. Two types of secure Luenberger-like distributed observers are proposed to estimate the system state and attack signal simultaneously. Specifically, the proposed two observers are applicable to deal with the cases in the presence and absence of time delays during network communication. It is also shown that the proposed observers can ensure the attack estimations from different agents asymptotically converge to the same value. Sufficient conditions for guaranteeing the asymptotic convergence of the estimation errors are derived. Simulation examples are finally provided to demonstrate the effectiveness of the proposed results.

Memory Saving State-Sharing Multi-Observer for a Class of Multi-Observer-Based Algorithms

A multi-observer is a bank of observers which is used for state estimation in various applications. However, it has an implementation bottleneck when a large number of observers are required for the desired estimation performance. To overcome this problem, we propose the design method of a state-sharing multi-observer for a class of nonlinear systems. The state-sharing multi-observer is a single observer that integrates a bank of observers, and its state size is independent of the number of observers. We analyze the error of the state obtained from the state-sharing multi-observer, and then show its applicability to multi-observer based algorithms such as supervisory observers and in secure state estimation.

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.

Climate-induced migrant's hopeful journey toward security: Pushing the boundaries of gendered vulnerability and adaptability in Bangladesh

Every year 10,000 climate-induced migrants in Bangladesh leave their homes seeking safer locations away from the climate-induced disasters they have experienced. They commonly migrate to nearby urban areas or the capital city after losing their livelihoods in their place of origin. However, the unplanned urbanization, limited capacities of urban infrastructures, service sector deficiencies, man-made disasters, and other social vulnerabilities further push these migrants into an (in)secure state. Hopes of security and capacity to adapt in their new homes can be impacted by the patriarchal society where gender is often associated with unequal social relations and hierarchies. These might extend from every day to long term (in)security. This study draws on qualitative data collected as part of research conducted for two PhD projects. In both cases, climate-induced migrants were forced to migrate from their places of origin due to sea level rise, river erosion, and soil salinity to Dhaka (capital city) and Coxes Bazar (coastal city) of Bangladesh. In this context, are their adaptive capacities influenced by gender relations? How are these adaptive capacities shaped through different institutions? And, how can these adaptive actions improve/strengthen human security? Gendered power relations are the main analytical framework for this paper as power is an influential factor to shape adaptive capabilities. It argues that (in)security, as an outcome of unsustainable adaptability, further pushes climate-induced migrants in vulnerable conditions in their newly settled urban areas. The vulnerability, capacity to adapt, and (in)security are gendered. This will contribute to understand for whom, where, and how the exclusive adaptative initiatives would further place the climate-induced migrants in vulnerable and (in)secure conditions in their newly settled areas.

Resilience to Passive Attacks of a Secure Key Distribution System Based on an Ultra-Long Fiber Laser Using a Bi-Directional EDFA

In this paper, we study the implementation of a secure key distribution system based on an ultra-long fiber laser with a bi-directional erbium-doped fiber amplifier. The resilience of the system was tested against passive attacks from an eavesdropper. A similarity was observed in the spectra for both secure configurations of the system and no signature that would allow an eavesdropper to obtain the secure state of the system was observed during the state transitions.

Secure state estimation for event-triggered cyber-physical systems against deception attacks

Nowadays, cyber-physical systems (CPSs) have been widely used in various fields due to their powerful performance and low cost. The cyber attacks will cause security risks and even huge losses according to the universality and vulnerability of CPSs. As a typical network attack, deception attacks have the features of high concealment and strong destructiveness. Compared with the traditional deception attack models with a constant value, a deception attack with random characteristics is introduced in this paper, which is difficult to identify. In order to defend against such deception attacks and overcome energy constraints in CPSs, the secure state estimation and the event-triggered communication mechanism without feedback information are co-considered to reconcile accuracy of estimation and energy consumption. Firstly, an event-triggered augmented state estimator is proposed for secure state estimation and attack identification. Then, under the ideology of equivalence, the augmented state estimator is derived as a concise two-stage estimator with reduced order. The two-stage estimator can perform the secure state estimation and attack identification respectively. The estimators ensure the accuracy of attack identification well since not treating attack information as the trigger event. Afterward, the comparison of the computational complexity of these two algorithms is analyzed. Finally, an example of a target tracking system is supplied to prove the effectiveness and efficiency of the proposed algorithm.

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 of Cyber-Physical System under Cyber Attacks: Q-Learning vs. SARSA

This paper proposes a reinforcement learning (RL) algorithm for the security problem of state estimation of cyber-physical system (CPS) under denial-of-service (DoS) attacks. The security of CPS will inevitably decline when faced with malicious cyber attacks. In order to analyze the impact of cyber attacks on CPS performance, a Kalman filter, as an adaptive state estimation technology, is combined with an RL method to evaluate the issue of system security, where estimation performance is adopted as an evaluation criterion. Then, the transition of estimation error covariance under a DoS attack is described as a Markov decision process, and the RL algorithm could be applied to resolve the optimal countermeasures. Meanwhile, the interactive combat between defender and attacker could be regarded as a two-player zero-sum game, where the Nash equilibrium policy exists but needs to be solved. Considering the energy constraints, the action selection of both sides will be restricted by setting certain cost functions. The proposed RL approach is designed from three different perspectives, including the defender, the attacker and the interactive game of two opposite sides. In addition, the framework of Q-learning and state–action–reward–state–action (SARSA) methods are investigated separately in this paper to analyze the influence of different RL algorithms. The results show that both algorithms obtain the corresponding optimal policy and the Nash equilibrium policy of the zero-sum interactive game. Through comparative analysis of two algorithms, it is verified that the differences between Q-Learning and SARSA could be applied effectively into the secure state estimation in CPS.

Dynamic Security Assessment For Power System Using Attribute Selection Technique

The evaluation of the dynamic security of the electrical power system after the occurrence of disturbances in the network is one of the most important tools that the control center uses to maintain the system in a safe operating mode, as well as prevent cases of system out of control and cases of complete shutdown. With the annual increase in the size of the electrical system and its distribution over a very wide geographical area, this led to a new challenge to assess dynamic security assessment (DSA), which is dealing with a huge and varied amount of data that requires processing in a very short time. To address these challenges, this study presented a new technique of artificial intelligence, which is the attribute selection technique, to reduce the size of this data and thus improve the accuracy and speed of results. This method relied on the combination of decision tree algorithms and a technique (Attribute selection) in the data obtained from the test system (IEEE-30Bus). The results of this method showed a significant reduction in the number of data used, which amounted to (45.55%) of the total data, Which led to an improvement in the classification accuracy, as the classification accuracy reached (97.27%). This reduction is very important when dealing in the online operating environment, as it saves the time necessary to reach the most accurate evaluation decision and thus issue gives a greater opportunity to take the appropriate decision in the event of disturbances and keep the electrical system in a secure state.

Observability Decomposition-Based Decentralized Kalman Filter and Its Application to Resilient State Estimation under Sensor Attacks.

This paper considers a discrete-time linear time invariant system in the presence of Gaussian disturbances/noises and sparse sensor attacks. First, we propose an optimal decentralized multi-sensor information fusion Kalman filter based on the observability decomposition when there is no sensor attack. The proposed decentralized Kalman filter deploys a bank of local observers who utilize their own single sensor information and generate the state estimate for the observable subspace. In the absence of an attack, the state estimate achieves the minimum variance, and the computational process does not suffer from the divergent error covariance matrix. Second, the decentralized Kalman filter method is applied in the presence of sparse sensor attacks as well as Gaussian disturbances/noises. Based on the redundant observability, an attack detection scheme by the test and a resilient state estimation algorithm by the maximum likelihood decision rule among multiple hypotheses, are presented. The secure state estimation algorithm finally produces a state estimate that is most likely to have minimum variance with an unbiased mean. Simulation results on a motor controlled multiple torsion system are provided to validate the effectiveness of the proposed algorithm.

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.

Resilient control of cyber‐physical systems using adaptive super‐twisting observer

AbstractIn this work, the problem of online secure state estimation and attack reconstruction in the face of offensives that corrupt the sensor measurements and modify the actuator commands of cyber–physical systems is investigated for designing a resilient controller for the system. The states of cyber–physical system and its actuator attacks are estimated/reconstructed online using a novel adaptive line‐by‐line super‐twisting observer, whereas sparse stealth attacks on unprotected sensors are reconstructed using a sparse recovery algorithm. The estimated attacks are used for attack compensation by a resilient controller. The efficacy of the proposed technique is illustrated via simulation on a real electric power system under deception actuator attack and stealth sensor attack.

Finite-Time Secure Dynamic State Estimation for Cyber–Physical Systems Under Unknown Inputs and Sensor Attacks

In this article, an efficient method for finite-time secure dynamic state estimation in cyber–physical systems (CPSs) subjected to unknown inputs and cyber-attacks is proposed. The proposed approach is based on a set of local finite-time state estimators operating over the subsets of sensory nodes, which are designed to estimate the states of the CPS subjected to unknown inputs. When cyber-attacks compromise some sensory nodes, the estimation results of the local finite-time estimators which use the measurements of the attacked sensors can be corrupted. An efficient detection algorithm is thus proposed to identify the valid local estimators that are completely devoid of the attacked sensory nodes. The information of the valid local estimators is then used to achieve secure state estimation and localization of the launched cyber-attack. The necessary and sufficient conditions for the feasibility and finite-time convergence of the proposed estimation mechanism are analytically derived and proven. The effectiveness of the proposed method is demonstrated by testing it on a dc electric motor. Likewise, some online software-in-the-loop tests are conducted to demonstrate the real-time feasibility of the proposed algorithm.

Efficient secure state estimation against sparse integrity attack for regular linear system

AbstractWe consider the problem of estimating the state of a time‐invariant linear Gaussian system in the presence of integrity attacks. The attacker can compromise out of sensors, the set of which is fixed over time and unknown to the system operator, and manipulate the measurements arbitrarily. Under the assumption that the system is regular and system matrix is non‐singular, we propose a secure estimation scheme that is resilient to ‐sparse attack as long as the system is ‐sparse detectable, which achieves the fundamental limit of secure dynamic estimation. In the absence of attack, the proposed estimation coincides with Kalman estimation with a certain probability that can be adjusted to trade‐off between performance with and without attack. Furthermore, the detectability condition checking in the designing phase and the estimation computing in the online operating phase are both computationally efficient. Two numerical examples including the IEEE 68 bus test system are provided to corroborate the results and illustrate the performance of the proposed estimator.

Real-Time Short-Term Voltage Stability Assessment Using Combined Temporal Convolutional Neural Network and Long Short-Term Memory Neural Network

This research presents a new method based on a combined temporal convolutional neural network and long-short term memory neural network for the real-time assessment of short-term voltage stability to keep the electric grid in a secure state. The assessment includes both the voltage instability (stable state or unstable state) and the fault-induced delayed voltage recovery phenomenon subjected to disturbance. The trained model uses the time series post-disturbance bus voltage trajectories as the input in order to predict the stability state of the power system in a computationally efficient manner. The proposed method also utilizes a transfer learning approach that acclimates to the pre-trained model using only a few labeled samples, which assesses voltage instability under unseen network topology change conditions. Finally, the performance evaluated on the IEEE 9 Bus and New England 39 Bus test systems shows that the proposed method gives superior accuracy with higher efficacy and thus is suitable for online application.