Attack-Resilient H_2, H_∞, and ℓ_1 State Estimator

Abstract

This paper considers the secure state estimation problem for noisy systems in the presence of sparse sensor integrity attacks. We show a fundamental limitation: that is, 2ρ-detectability is necessary for achieving bounded estimation errors, where ρ is the number of attacks. This condition is weaker than the 2ρ-observability condition typically assumed in the literature. Conversely, we propose a real-time state estimator that achieves the fundamental limitation. The proposed state estimator is inspired by robust control and FDI: that is, it consists of local Luenberger estimators, local residual detectors, and a global fusion process. We show its performance guarantees for H_2, H_∞, and ℓ_1 systems. Finally, numerical examples show that it has relatively low estimation errors among existing algorithms and average computation time for systems with a sufficiently small number of compromised sensors.