This paper studies the problem of designing the optimal deception attack to maximize a utility function with the Kullback-Leibler divergence adopted as a detection constraint. The utility function reflects the goal of pulling the state away from the origin, increasing the cost of the controller and decreasing the cost of the attacker. To analyze the stealthiness of the attack, the attack signal is decomposed into two parts, one of which is strict stealthy. The necessary and sufficient condition is derived for the case that the strict stealthy attack cannot lead to an unbounded benefit. In this case, the linear transformation of the optimal attack is proved to be a Gaussian distribution. With the mean value and covariance of the Gaussian distribution as variables, the original problem is transformed into a new problem which may not be convex. A suboptimal attack policy is provided and the upper bound for the loss of benefit when using the suboptimal attack is also given. A numerical example of unmanned ground vehicle is illustrated to verify the effectiveness of the proposed attack policy.

This paper addresses the problem of designing a distributed filter for linear discrete-time networked control systems that suffer from randomly occurring deception attacks and bounded disturbances. A Round-Robin-type protocol is applied to schedule communication between filters due to the communication resource constraint. The discrete-time Wirtinger's inequality is used to derive a sufficient condition that ensures H∞ performance of the closed-loop system. A corresponding filter that guarantees the security is designed. Finally, a numerical example of an inverted pendulum system is provided to demonstrate the feasibility of the proposed filter.

This article presents an event-triggered distributed model predictive control with variable prediction horizon strategy for spatially interconnected systems with input and state constraints. Each subsystem compares the error between actual state and optimal state with a triggering level, and cooperates with other subsystems to determine the triggering time and the corresponding prediction horizon. A shrinking constraint related to the bounds of errors between the predicted states and the optimal states of the previous triggering time instant is introduced into the optimization problem. By implementing the proposed strategy, the number of optimization problems that need to be solved is decreased, and the complexity of the optimization problem is reduced with the actual state approaching the terminal set. The feasibility of the optimization problem and the asymptotic stability of the closed-loop system are established. Finally, the simulation results show that the proposed strategy works well.

This paper investigates the design of stealthy deception attacks with the aim of destroying the estimate performance without knowing the filter gain. The residual used to detect attacks is generated by the parity space approach and the Kullback-Leibler divergence is adopted as the metric of stealthiness. We first give the necessary and sufficient condition for the inexistence of the strictly stealthy attack, which does not change the residual and can lead to unbounded estimate error. When the strictly stealthy attack does not exist, a lower bound of the secondary moment of the estimate error is then derived via the posterior Cramer-Rao bound. The zero-mean Gaussian attack that maximizes this lower bound is obtained by solving a convex optimization problem. The proposed method can also be applied to design stealthy attacks with the aim of destroying the control performance. Finally, a numerical example of longitudinal flight control system is illustrated to demonstrate the effectiveness of the proposed attack.

This article studies the reachable set of cyber-physical systems subject to stealthy attacks with the Kullback-Leibler divergence adopted to describe the stealthiness. The reachable set is defined as the set in which both the system state and the estimation error of the Kalman filter reside with a certain probability. The necessary and sufficient conditions of the reachable set being unbounded are given for the finite and infinite time cases, respectively. When the reachable set is bounded, an ellipsoidal outer approximation is obtained by solving a convex optimization problem. An application of this approximation to the safety evaluation is also given. A numerical simulation of an unmanned ground vehicle is presented to demonstrate the effectiveness of the proposed approach.

This article investigates the design of online stealthy attacks with the aim of moving the system's state to the desired target. Different from the design of offline attacks, which is only based on the system's model, to design the online attack, the attacker also estimates the system's state with the intercepted data at each instant and computes the optimal attack accordingly. To ensure stealthiness, the Kullback–Leibler divergence between the innovations with and without attacks at each instant should be smaller than a threshold. We show that the attacker should solve a convex optimization problem at each instant to compute the mean and covariance of the attack. The feasibility of the attack policy is also discussed. Furthermore, for the strictly stealthy case with zero threshold, the analytical expression of the unique optimal attack is given. Finally, a numerical example of the longitudinal flight control system is adopted to illustrate the effectiveness of the proposed attack.