Biblio

Cyber-physical systems are vulnerable to attacks that can cause them to reach undesirable states. This paper provides a theoretical solution for increasing the resiliency of control systems through the use of a high-authority supervisor that monitors and regulates control signals sent to the actuator. The supervisor aims to determine the control signal limits that provide maximum freedom of operation while protecting the system. For this work, a cyber attack is assumed to overwrite the signal to the actuator with Gaussian noise. This assumption permits the propagation of a state covariance matrix through time. Projecting the state covariance matrix on the state space reveals a confidence ellipse that approximates the reachable set. The standard deviation is found so that the confidence ellipse is tangential to the danger area in the state space. The process is applied to ship dynamics where an ellipse in the state space is transformed to an arc in the plane of motion. The technique is validated through the simulation of a ship traveling through a narrow channel while under the influence of a cyber attack.