Distributed Resilient Estimator Design for Positive Systems Under Topological Attacks

This article is concerned with the distributed resilient estimation of a positive system over a sensor network. First, a heterogeneous sensor interaction framework, where each sensor is capable of sharing its local information of measurement as well as state estimate with its underlying neighbors via distinct interaction topologies, is proposed to account for different sensor communication capacities. During the information exchanges among the sensors, topological attacks are suitably modeled in such a way to incorporate the random and intermittent disruption of the heterogeneous sensor interaction topologies. Second, two sets of distributed resilient estimators are delicately constructed to cope with the resulting random denial of information exchanges within the specific repaired periods and compromised periods caused by the topological attacks. Third, the resilience performance analysis with a prescribed <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">l</i> <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1</sub> -gain attenuation level is carried out, and a linear programming approach is then developed to achieve the design of the desired distributed estimators. Finally, the effectiveness of the proposed design method is verified through a vehicle formation monitoring system.