Attack-resilient Estimation of Switched Nonlinear Stochastic Cyber-Physical Systems

This paper studies attack-resilient estimation of a class of switched nonlinear systems subject to stochastic noises. The systems are threatened by both of signal attacks and switching attacks. The problem is formulated as the joint estimation of states, attack vectors and modes of hidden-mode switched systems. We propose an estimation algorithm which is composed of a bank of state and attack vector estimators and a mode estimator. The mode estimator selects the most likely mode based on modes' posterior probabilities induced by the discrepancies between obtained outputs and predicted outputs. We formally analyze the stability of estimation errors in probability for the proposed estimator associated with the true mode when the hidden mode is time-invariant but remains unknown. For hidden-mode switched linear systems, we discuss a way to reduce computational complexity which originates from unknown signal attack locations. Lastly, we present numerical simulations on the IEEE 68-bus test system to show the estimator performance for time-varying modes with a regular mode set and a reduced mode set.