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

TL;DR

This paper introduces an attack-resilient estimation method for switched nonlinear stochastic cyber-physical systems, capable of jointly estimating states, attack vectors, and modes under stochastic noise and attack conditions.

Contribution

It proposes a novel estimation algorithm combining multiple estimators and a mode selector, with formal stability analysis and reduced complexity for certain systems.

Findings

Estimator effectively detects and estimates attacks in simulations.

Stable estimation errors in probability for time-invariant modes.

Reduced computational complexity for switched linear systems.

Abstract

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.