Learning-based minimum cost strategies for set reachability of Boolean control networks under data injection attacks

This paper investigates false data injection attacks (FDIAs) with failure probabilities in set reachability of Boolean control networks. Necessary and sufficient conditions are established for the existence of data injection sequences (DISs) that ensure set reachability with probability one or above a given bound under any control input sequence (CIS) within a predefined time. Moreover, for all CISs and DISs, corresponding conditions are derived to guarantee set reachability under the same probabilistic bounds. In addition, for specific CISs, a newly constructed system is proposed, based on which a necessary and sufficient condition is established for the existence of DISs that ensure set reachability with probability one within the predefined time. Subsequently, an algorithm is proposed to obtain a minimum time DIS that achieves set reachability. To handle large-scale networks without an explicit system model, a method based on double deep Q network is introduced to obtain a DIS that achieves set reachability with minimal cost. Finally, several biological examples demonstrate the practicality and effectiveness of the proposed methodology.