Observer-based resilient control of positive systems with heterogeneous DoS attacks: A Markov model approach

This paper investigates the problem of observer-based resilient control of positive systems with heterogeneous DoS attacks. As the attack strategy becomes more and more intelligent, the DoS attacks may be heterogeneous, which means the attack probability and attack success rate of the heterogeneous DoS attacks are time-varying. Different from the existing uniform DoS attacks, the heterogeneous DoS attacks can not be described accurately by the marginal probability. In this paper, a Markov model approach is proposed to describe the heterogeneous DoS attacks with a particular form of transition probability. Based on the obtained Markov model, a output-feedback observer is designed to estimate the missing sensor data. Then, the mode-dependent observer-based resilient controllers of positive systems are designed to against the heterogeneous DoS attacks. Moreover, the positivity and stability of the positive system with L1 performance are analyzed under heterogeneous DoS attacks. In the end, to verify the validity, the proposed approach is applied to continuous stirred tank reactor(CSTR) and age-structured population model.