Security Analysis of Cluster Synchronization for Boolean Control Networks Under Deception Attacks

This paper investigates the security of cluster synchronization in Boolean control networks under deception attacks, where attackers manipulate system states to disrupt feedback controller selections. Using an equivalent algebraic framework, the evolution of state feedback controllers under deception attacks is analyzed, and secure invariant subsets are introduced to recast security issues as set stability problems. Some necessary and sufficient conditions are established for both finite-time and asymptotic cluster synchronization under attacks. To avoid computationally intensive high-dimensional matrix operations, a state-space partitioning method is proposed for verifying finite-time cluster synchronization security. In addition, a trajectory-set-sequence approach for assessing asymptotic cluster synchronization security is proposed. Furthermore, two criteria are derived for the existence of feedback gain matrices that guarantee finite-time and asymptotic cluster synchronization, respectively, under deception attacks. Finally, numerical simulations validate the effectiveness of the proposed methods.