Based on frequency-domain transformation technique, this paper proposes an attack detection scheme for stochastic control systems under stochastic cyber-attacks and disturbances. The focus is on designing an anomaly detector for the stochastic control systems. First, we construct a model of stochastic control system with stochastic cyber-attacks which satisfy the Markovian stochastic process. And we also introduced the stochastic attack models that a control system ispossibly exposed to. Next, based on the frequency-domain transformation technique and linear algebra theory, we propose an algebraic detection scheme for a possible stochastic cyber-attack. We transform the detector error dynamic equation into an algebraic equation. By analyzing the rank of the stochastic matrix E(Q (z0)) in the algebraic equation, residual information is obtained and anomalies in the stochastic system are detected. In addition, sufficient and necessary conditions guaranteeing the detectability of the stochastic cyber-attacks are obtained. The presented detection approach in this paper is simple, straightforwardand more ease to implement. Finally, the results are applied to some physical systems that are respectively subject to a stochastic data denial-of-service (DoS) attack and a stochastic data deception attack on the actuator. The simulation results underline that the detection approach is efficient and feasible in practical application.
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