Distributed Resilient Observer: Blended Dynamics Theory Meets ℓ1-Minimization Approach

Abstract

This paper presents a distributed resilient observer for continuous-time linear time-invariant plants that remains functional even under sensor attacks. The proposed method aims to determine the estimation outcome that matches the majority of sensor measurements, which is formulated as an ℓ1-minimization problem considering all the observable components of each sensor measurement. A distributed observer based on the blended dynamics theory is then proposed to solve the ℓ1-minimization problem in a distributed manner. As a result, the distributed resilient estimation is enabled for a broader class of systems compared to previous works. The design procedure is constructive with parameters obtained from a specified condition that is equivalent to the well-known null-space property.