Shifting Attack Stabilization and Estimation of Hidden Markov Boolean Networks

In this article, a network attack, named shifting attack, is considered for hidden Markov Boolean control networks (HMBCNs). Using semi-tensor product of matrices, the considered network and the network attack are presented in algebraic form. State feedback control (SFC) is then applied to stabilize the considered network to a desired state. A necessary and sufficient condition based on the probability matrix is presented for the stochastic stabilization of the HMBCN, based on which, the design of the SFC is given. Then shifting attack is further studied for HMBCNs. The control strategy will be shifted to another when the HMBCN is under attack. Shifting attack is also modeled in a hidden Markov process, under which, a necessary and sufficient condition for the security of the attacked HMBCN is also presented. Propositions are obtained for the security and insecurity of the attacked HMBCN. Using the change of the probability measurement approach, estimations of the states expectation and the attacked signals expectation for the attacked HMBCN are solved. At last, examples show the effectiveness of the obtained results.