An Optimal Design of a Moving Target Defense for Attack Detection in Control Systems

In this paper, we consider the problem of designing system parameters to improve detection of attacks in control systems. Specifically, we study control systems which are vulnerable to integrity attacks on sensors and actuators. We aim to defend against strong model aware adversaries that can read and modify all sensors and actuators. Previous work has proposed a moving target defense for detecting integrity attacks on control systems. Here, an authenticating subsystem with time-varying dynamics coupled to the original plant is introduced. Due to this coupling, an attack on the original system will affect the authenticating subsystem and in turn be revealed by a set of sensors measuring the extended plant. Moreover, the time-varying dynamics of the extended plant act as a moving target, preventing an adversary from developing an effective adaptive attack strategy. Previous work has failed to consider the design of the time-varying system matrices and as such provides little in terms of guidelines for implementation in real systems. This paper proposes two optimization problems for designing these matrices. The first designs the auxiliary actuators to maximize detection performance while the second designs the coupling matrices to maximize system estimation performance. Numerical examples are presented that validate our approach.