• absorbing probability
• agreement
• consensus
• consensus network
• intruders
• markov chain
• network
• security
• sensors network
• sthocastic matrix
• unknown input obervability

This work focuses on trustworthy computation systems and proposes a
novel intrusion detection scheme for consensus networks with misbehaving
nodes. This prototypical control problem is relevant in network security
applications. The objective is for each node to detect and isolate the
misbehaving nodes using only the information flow adopted by standard
averaging protocols. We focus mainly on the single misbehaving node problem.
Our technical approach is based on the theory of Unknown Input
Observability. First, we give necessary and sufficient conditions for
the misbehavior to be observable and for the identity of the faulty node
to be detectable. Second, we design a distributed unknown input
estimator, and we characterize its convergence rate in the
"equal-neighbor" model and in the general case. Third and finally, we
propose a complete detection and isolation scheme and provide some
remarks on the filter convergence time. We also analyze the multiple misbehaving nodes problem, and we describe an algorithm to deal with it. We conclude the document with the numerical study of a consensus problem, of a robot deployment problem, and of an averaging problem.