Enhancement of opacity for distributed state estimation in cyber–physical systems

Abstract

Opacity, a confidentiality property that characterizes whether a “secret” of a system can be inferred by an outside intruder, is an increasing concern in cyber–physical systems (CPSs). The existing distributed estimation algorithms allow each node to broadcast its explicit state information to its neighbors, which results in the disclosure of CPS’s secret state. To meet the confidentiality requirement, this paper formulates a new framework for opacity for distributed state estimation. Two opacity-enhancing algorithms are proposed against the intruder models with different eavesdropping capacities for a subset of nodes. Necessary and sufficient conditions to ensure that a secret state is opaque are established in terms of the rank of constructed structural matrices of the eavesdropped nodes. Moreover, it is shown that the use of enhancement mechanism does not compromise the estimation accuracy. The framework of opacity is further extended to the case of measurement noises.