A secure state estimation algorithm for nonlinear systems under sensor attacks

TL;DR

This paper proposes a robust state estimation algorithm for nonlinear systems under sensor attacks, ensuring asymptotic convergence of estimates despite malicious sensor data, with practical application to power networks.

Contribution

It introduces a sufficient condition for observability under sensor attacks in nonlinear systems and provides a constructive method to design robust observers.

Findings

Algorithm achieves asymptotic state reconstruction under attacks.

Provides a constructive design method for robust observers.

Demonstrates application to power distribution network monitoring.

Abstract

The state estimation of continuous-time nonlinear systems in which a subset of sensor outputs can be maliciously controlled through injecting a potentially unbounded additive signal is considered in this paper. Analogous to our earlier work for continuous-time linear systems in \cite{chong2015observability}, we term the convergence of the estimates to the true states in the presence of sensor attacks as `observability under $M$ attacks', where $M$ refers to the number of sensors which the attacker has access to. Unlike the linear case, we only provide a sufficient condition such that a nonlinear system is observable under $M$ attacks. The condition requires the existence of asymptotic observers which are robust with respect to the attack signals in an input-to-state stable sense. We show that an algorithm to choose a compatible state estimate from the state estimates generated by the bank of observers achieves asymptotic state reconstruction. We also provide a constructive method for a class of nonlinear systems to design state observers which have the desirable robustness property. The relevance of this study is illustrated on monitoring the safe operation of a power distribution network.