Robust algorithm for attack detection based on time-varying hidden Markov model subject to outliers

The problem of robust attack detection and prediction for networked control systems in the presence of outliers is discussed in this article. The conventional hidden Markov model (HMM) is trained to learn the system behavior (ie, transitions between different operating modes) in the nominal process. The HMM with time-varying transition probabilities is used to track the attack behavior in which the adversary triggers more hazard modes to hasten fatigue of control devices by injecting attack signals with random magnitude and frequency. For different operating modes, the observations are assumed to follow different multivariate Student'stdistributions instead of Gaussian distributions and thus address the robust estimation problem. The expectation maximization algorithm is used to estimate parameters. Finally, simulations are conducted to verify the effectiveness of the proposed method.