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

This letter 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
$\ell _{1}$
-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
$\ell _{1}$
-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.