Security analysis of continuous-time cyber-physical system against sensor attacks

Abstract

This paper investigates the secure state estimation problem for a continuous-time Gauss-Markov system, where the physical plant is observed by m sensors and a subset of the sensors can potentially be compromised by an adversary. Under mild assumptions, we prove that the continuous-time optimal Kalman estimate can be decomposed as a weighted sum of local state estimates, each of which is computed using only the measurements from a single sensor. Then a convex optimization based approach is proposed to generate a more secure state estimate based on these local estimates. We provide a sufficient condition under which the proposed estimator is stable against the attack when less than half of the sensors are compromised. Finally, a numerical example is provided to illustrate the performance of the proposed secure state estimation scheme.