Synthesis of Optimal Stealthy Attacks against Diagnosability in Labeled Petri Nets

This paper addresses the diagnosability analysis problem under external malicious attacks of a networked discrete event system modeled by labeled Petri net. In particular, we focus on a stealthy replacement attack to alter or corrupt the observation of the system, in which the transition labels are replaced by others or empty string, and its attack stealthiness requires that the corrupted observations should be contained in the behavior of system. The aim of this work is, from an attacker viewpoint, to design a stealthy replacement attack for violating the diagnosability of system. To this end, we first build a new structure, called complete unfolded verifier, with the notion of a predefined elementary unsound path that leads to the violation of diagnosability, which is used to enumerate all the potential attacked paths to be transformed into elementary unsound ones. Then an optimal attack synthesis problem in terms of minimum energy cost is formulated by determining whether an elementary unsound path is generated via solving a set of integer nonlinear programming problems. Finally, we show that the nonlinear programming problems can be transformed into integer linear programming problems by introducing additional linear constraints. Examples are used to illustrate the proposed attack strategy.