Distributed Krein space-based attack detection over sensor networks under deception attacks

This paper is concerned with distributed attack detection for a discrete time-varying system monitored by a sensor network. An adversary simultaneously launches distinct data deception attacks on both the system dynamics and sensor intercommunication links so as to intentionally falsify the system state and the exchanged sensor measurement outputs. First, delicate distributed estimators are constructed, aiming to provide resilient local estimates for unavailable system state and appropriate residuals for attack detection. Second, an auxiliary Krein space state–space model as well as innovation analysis and a projection technique is skillfully employed to cast the finite horizon distributed estimator design problem into a minimization problem of a certain indefinite quadratic form. A necessary and sufficient condition on the existence of the minimum is derived. Third, a computational efficient recursive algorithm is developed to design desired distributed estimators such that the local estimates and residuals can be both determined at each time step. Furthermore, a two-stage distributed detection mechanism is proposed for each estimator to alert the attack occurrence. Specifically, it is shown that by properly choosing a weighting matrix parameter, each estimator can respectively detect the deception attacks launched on the system layer and sensor intercommunication links. Finally, the effectiveness of the proposed approach is demonstrated through numerical verification.