State Estimation In Cyber-physical Systems Research Articles

Optimal design and allocation of stealthy attacks against remote state estimation for cyber-physical systems

This paper studies the design and allocation problem for stealthy attacks against remote state estimation for cyber-physical systems, where the data are transmitted through multiple wireless communication channels. With limited budget for the available energy at each step and total energy over the finite-time horizon, the aim of the stealthy attacker is to maximize the estimation error based on the collaboration between the attack matrices and schedule, which is formulated as the optimization problem with multi-variable coupling. Under the presented framework of stepwise optimization, the optimization problem is separated into two subproblems with the guarantee of optimality. First, for the optimal design of attack matrices, the analytical expression is derived by employing the proposed data isolation technique instead of the assumption utilized in the existing results that the output matrix is of full row rank. And then, for the optimal allocation of energy constrained attacks, the scheduling sequence is obtained by solving the transformed linear 0-1 programming. Finally, simulation results sustain the performance of the presented attack strategy.

Optimal Stealthy Attacks With Energy Constraint Against Remote State Estimation.

This article investigates the problem of energy-constrained stealthy attack strategy against remote state estimation for cyber-physical systems. Taking into account the energy constraint, the malicious attacker is required to schedule the off-line generated signals to modify the transmitted data with limited times over a finite-time horizon under the stealthiness condition, which makes the design of attack strategy more complex. Different from the attack schedules which are studied on the basis of prescribed attack signals in the existing results, the attack strategy is presented under the framework of collaborative design to deteriorate the estimation performance to the largest extent, which yet leads to the coupling between the attack schedules and attack signals. To overcome the difficulty without sacrificing the optimality, the attack design problem is solved in two steps. First, analyze the problem with the given attack schedule to derive the optimal attack signals. Then, the optimal schedule is obtained by efficiently solving the nonlinear 0-1 programming problem based on the algorithm of reducing the search space which is designed to eliminate a part of the nonoptimal solutions. To demonstrate the theoretical results, a simulation example is provided.

Secure state estimation for cyber-physical systems with unknown input sliding mode observer

Secure state estimation for cyber-physical systems with unknown input sliding mode observer

Lasso-based state estimation for cyber-physical systems under sensor attacks

The development of algorithms for secure state estimation in vulnerable cyber-physical systems has been gaining attention in the last years. A consolidated assumption is that an adversary can tamper a relatively small number of sensors. In the literature, block-sparsity methods exploit this prior information to recover the attack locations and the state of the system. In this paper, we propose an alternative, Lasso-based approach and we analyse its effectiveness. In particular, we theoretically derive conditions that guarantee successful attack/state recovery, independently of established time sparsity patterns. Furthermore, we develop a sparse state observer, by starting from the iterative soft thresholding algorithm for Lasso, to perform online estimation. Through several numerical experiments, we compare the proposed methods to the state-of-the-art algorithms.

Double Threshold Structure of Sensor Scheduling Policy Over a Finite-State Markov Channel.

In this article, we consider the optimal sensor scheduling for remote state estimation in cyber-physical systems (CPSs). Different from the existing works concerning the time-invariant channel state in the wireless communication network, our work considers the time-varying channel state modeled by a finite-state Markov channel (FSMC). We focus on the problem of how to schedule the transmission of the sensor to minimize the estimation error at the remote side with less communication cost. Using the framework of the Markov decision process (MDP), the optimal scheduling policy is shown to be deterministic stationary (DS). We further derive its double threshold structure with respect to remote estimation errors and channel states. Moreover, a necessary and sufficient condition guaranteeing the mean-square stability of the remote estimator is given based on the structured scheduling policy. Numerical simulations are provided to verify the theoretical results.

Secure state estimation for cyber-physical systems by unknown input observer with adaptive switching mechanism

A new state estimation method is proposed in this manuscript for a class of linear cyber-physical systems (CPSs) with sparse sensor attacks, unknown input and output disturbances. The sensor attack will make part of the measurement signal received by the remote observer inaccurate. In order to achieve the secure state estimation (SSE) for the investigated linear CPSs, an unknown input observer (UIO) with adaptive switching mechanism is designed. Inspired by the existing results, a set of sub-observers is designed which can exclude the influence of unknown input and output disturbances. To achieve switching between different sub-observers, the adaptive switching mechanism is designed according to the switching adversarial principle. Some parameters of the observer are obtained by designing a set of linear matrix inequalities (LMIs). The sufficient condition for the existence of the observer and the proof of its effectiveness are respectively given by theoretical analysis. Finally, the effectiveness of the proposed method is proved by two Matlab simulation experiments.

Optimal acknowledgment signal attacks against remote estimation

In this paper, we consider a malicious attack issue against remote state estimation in cyber-physical systems. Due to the limited energy, the sensor adopts an acknowledgment-based (ACK-based) online power schedule to improve the remote state estimation. However, the feedback channel will also increase the risk of being attacked. The malicious attacker has the ability to intercept the ACK information and modify the ACK signals (ACKs) from the remote estimator. It could induce the sensor to make poor decisions while maintaining the observed data packet acceptance rate to keep the attacker undetected. To maximize the estimation error, the attacker will select appropriate attack times so that the sensor makes bad decisions. The optimal attack strategy based on the true ACKs and the corrosion ACKs is analytically proposed. The optimal attack time to modify the ACKs is the time when the sensor’s tolerance, i.e., the number of consecutive data packet losses allowed, is about to reach the maximum. In addition, such an optimal attack strategy is independent of the system parameters. Numerical simulations are provided to demonstrate the analytical results.

False data injection attacks on sensors against state estimation in cyber-physical systems

In this paper, the problem about the false data injection attacks on sensors to degrade the state estimation performance in cyber-physical systems(CPSs) is investigated. The attack strategies for unstable systems and stable ones are both designed. For unstable systems, based on the idea of zero dynamics, an unbounded attack strategy is proposed which can drive the state estimation error variations to infinity. The proposed method is more general than existing unbounded attack strategies since it relaxes the requirement for the initial value of the estimation error. For stable systems, it is difficult to bring unbounded impacts on the estimation error variations. Therefore, in this case, an attack strategy with adjustable attack performance which makes the estimation error variations track predesigned target values is proposed. Furthermore, a uniform attack strategy which aims to deteriorate state estimation for both stable systems and unstable ones is derived. Finally, simulations are provided to illustrate the effectiveness of the proposed attack strategies.

On Two Sensors Scheduling for Remote State Estimation With a Shared Memory Channel in a Cyber-Physical System Environment.

This article studies two sensors scheduling with a shared memory channel for remote state estimation in cyber-physical systems (CPSs). We consider that each sensor monitors a plant and sends its local estimate to the remote estimator over a shared memory communication channel, of which the packet reception results between two successive time instants are correlated. This article focuses on how the two sensors are scheduled to minimize the total estimation errors at the remote side. The problem is formulated as the Markov decision process (MDP) and the optimal policy is derived. Moreover, the threshold structure of the optimal policy is given to reduce computation overhead. After proving the Whittle indexability of the overall system under a given condition, the Whittle index policy is adopted to further reduce the computation overhead. Numerical simulations are given to illustrate the theoretical results.

Optimal transmission scheduling for remote state estimation in CPSs with energy harvesting two-hop relay networks

This paper considers the optimal transmission power scheduling for accurate remote state estimation in cyber–physical systems (CPSs). The plant is modeled as a discrete-time stochastic linear system with sensor measurements transmitted to the remote estimator over an intelligent relay. A dynamic cooperative team is formulated in which the sensor and the relay sharing the same cost function are equipped with corresponding energy harvesters, and need to decide on the transmission power levels to minimize the average error covariance at the remote estimator. Since the nodes make simultaneous decisions to achieve a common goal, the sensor and the relay do not have access to the transmission power that will be selected by another node in advance, and hence they cannot build a value estimation of the cost function directly at each time point, which poses a challenge to determine the optimal transmission policies of both sides. To overcome this challenge, we provide a local-action value function and prove that both nodes select the transmission power with respect to the local-action value function without any loss of performance. In addition, a Markov decision process (MDP) and a multi-agent reinforcement learning algorithm are presented to obtain the optimal transmission power schedule over an infinite time horizon. Finally, simulation examples are provided to corroborate and illustrate the theoretical results.

Secure State Estimation of Nonlinear Cyber-Physical Systems Against DoS Attacks: A Multiobserver Approach.

This article focuses on the problem of secure state estimation for cyber-physical systems (CPSs), whose physical plants are modeled as nonlinear strict-feedback systems. The measured output is sent to the designed observer over a wireless communication network subject to denial-of-service (DoS) attacks. Due to the energy constraints of the attackers, the attack duration is upper bounded. Under DoS attacks, the transmission is prevented, which worsens the estimation accuracy of the existing nonlinear observers significantly. To maintain the estimation performance, a novel multiobserver scheme and a switched algorithm are proposed by introducing the hold-input mechanism and the cascade observer technique. In comparison to the existing results, where the estimation error systems may be unstable during the attack time interval, the estimation error of the designed observer converges exponentially, such that the estimation performance is improved effectively. Finally, the theoretical findings are illustrated by simulation results.

Analysis of Replay Attacks with Countermeasure for State Estimation of Cyber-Physical Systems

Analysis of Replay Attacks with Countermeasure for State Estimation of Cyber-Physical Systems

Optimal Stealthy Joint Attacks against Distributed State Estimation in Cyber-Physical Systems

Optimal Stealthy Joint Attacks against Distributed State Estimation in Cyber-Physical Systems

Multisensor Scheduling for Remote State Estimation Over a Temporally Correlated Channel

This article studies multisensor scheduling for remote state estimation in cyber-physical systems. We consider that each sensor monitors a dynamic process and sends its data to the remote end. This article focuses on minimizing remote estimation errors over a temporally correlated communication channel. The problem is formulated as the Markov decision process (MDP) with finite-horizon cost criterion. The optimal structured policies are derived for both Markov packet dropout and finite-state Markov channel models, which can reduce computation overhead. For the infinite-horizon case, we design algorithms to address the issues of unknown channel statistics and the curse of dimensionality in the MDP, respectively. Particularly, a heuristic algorithm with linear complexity is proposed to schedule multisensor in a decentralized manner. Simulation examples are provided to verify the theoretical results.

Distributed Resilient State Estimation for Cyber-Physical Systems Against Bit Errors: A Zonotopic Set-Membership Approach

This paper addresses the distributed resilient state estimation issue for a class of large-scale cyber-physical systems (CPSs) against bit errors. Owing to the reliability of the binary data, a novel binary encoding-decoding scheme is developed to enable digital communication of the CPSs. We consider the situation where the transmitted binary bits may be flipped over noisy communication channels. The primary purpose of this paper is to design a distributed resilient estimation scheme under a bit-flipped detection mechanism to achieve a reliable estimation of the CPSs. First, by means of the Minkowski sum of sets, a novel distributed zonotopic resilient estimation scheme is proposed where the optimal estimator gain is obtained in the minimum <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$F$</tex-math></inline-formula> -radius sense. Furthermore, a two-stage bit-flipped detection scheme is developed by taking advantage of 1) the prediction output zonotope and 2) the intersection between the prediction zonotope and the estimation zonotope. Furthermore, in order to improve the algorithm efficiency, a reduction operator is introduced to reduce the order of the zonotope. Finally, the IEEE 30-bus systems are applied to verify theoretical results of the developed distributed resilient estimation algorithm.

Event-triggered state estimation for cyber-physical systems with partially observed injection attacks

Event-triggered state estimation for cyber-physical systems with partially observed injection attacks

Security Investment in Cyber-Physical Systems: Stochastic Games With Asymmetric Information and Resource-Constrained Players

This article considers remote state estimation in cyber-physical systems (CPSs) with multiple sensors. Each plant is modeled by a discrete-time stochastic linear system with measurements of each sensor transmitted to the corresponding remote estimator over a shared communication network when their securities are interdependent due to network-induced risks. A dynamic nonzero-sum game with asymmetric information is formulated in which each sensor subject to a resource budget constraint needs to decide whether to invest in security for sending data packets, taking the behaviors of other sensors into account. To overcome the difficulty in characterizing or computing the Nash equilibria (NE), the game with asymmetric information is transformed into another game with symmetric information such that the equilibrium of the original game can be obtained by solving the equilibrium of the new game. Under certain conditions, we devise a backward induction algorithm to obtain a subclass of NE of the original game, known as common information-based Markov perfect equilibria (CIBMPE). Finally, a numerical example is provided to illustrate the results obtained.

Security State Estimation for Cyber-Physical Systems against DoS Attacks via Reinforcement Learning and Game Theory

This paper addressed the optimal policy selection problem of attacker and sensor in cyber-physical systems (CPSs) under denial of service (DoS) attacks. Since the sensor and the attacker have opposite goals, a two-player zero-sum game is introduced to describe the game between the sensor and the attacker, and the Nash equilibrium strategies are studied to obtain the optimal actions. In order to effectively evaluate and quantify the gains, a reinforcement learning algorithm is proposed to dynamically adjust the corresponding strategies. Furthermore, security state estimation is introduced to evaluate the impact of offensive and defensive strategies on CPSs. In the algorithm, the ε-greedy policy is improved to make optimal choices based on sufficient learning, achieving a balance of exploration and exploitation. It is worth noting that the channel reliability factor is considered in order to study CPSs with multiple reasons for packet loss. The reinforcement learning algorithm is designed in two scenarios: reliable channel (that is, the reason for packet loss is only DoS attacks) and unreliable channel (the reason for packet loss is not entirely from DoS attacks). The simulation results of the two scenarios show that the proposed reinforcement learning algorithm can quickly converge to the Nash equilibrium policies of both sides, proving the availability and effectiveness of the algorithm.

Optimal innovation-based deception attacks with side information against remote state estimation in cyber-physical systems

In this paper, the problem of designing the optimal deception attacks against the remote state estimation in cyber-physical systems is investigated in the scenario where the attacker has the ability to acquire the side information about the system by employing an extra sensor. To degenerate the remote estimation performance, the attacker replaces the transmitted signals with the combination of the innovations from the system sensor and the extra sensor. Under the proposed attacks, the recursion of the error covariance of the remote estimates is derived by utilizing the orthogonality principle and the statistical properties of the related random variables. Then, the design of the attacks is transformed into a quadratic multivariate optimization problem and the optimal distribution of the modified innovations is found by taking advantage of the Lagrange multiplier method. Based on this, it is proved that the optimal policy is the solution to a semi-definite programming (SDP) problem, which results in the largest estimation errors and maintains the deceptiveness concurrently. Finally, simulation examples are given to verify the effectiveness of this work.

Event-triggered remote state estimation for cyber-physical systems under malicious DoS attacks

This paper focuses on the problem of event-triggered remote state estimation for cyber-physical systems (CPSs) under malicious denial-of-service (DoS) attacks. A remote estimator with intermittent observations is derived, and a novel event-triggered communication strategy is designed by transmitting observations to the remote estimator when the predicted estimation error covariance exceeds a given threshold. By constraining the upper bound of the total attack ratio, sufficient conditions to guarantee the almost sure stability of the proposed estimator are presented. Furthermore, the event-triggering parameter is designed to balance the estimation performance and the network resource utilization. In contrast to the previous studies on remote state estimation with random packet losses, the considered DoS attack case is more challenging since the probabilistic property of the packet loss process is unavailable to describe the attacks. Finally, the efficiency of the presented method is illustrated by simulation results.