System identification with binary-valued observations under both denial-of-service attacks and data tampering attacks:defense scheme and its optimality

In this paper,we investigate the defense problem against the joint attacks of denial-of-service attacks and data tampering attacks in the framework of system identification with binary-valued observations.By estimating the key parameters of the joint attack and compensating them in the identification algorithm,a compensation-oriented defense scheme is proposed.Then the identification algorithm of system parameter is designed and is further proved to be consistent.The asymptotic normality of the algorithm is obtained,and on this basis,we propose the optimal defense scheme.Furthermore,the implementation of the optimal defense scheme is discussed.Finally,a simulation example is presented to verify the effectiveness of the main results.