Robust Detection of Biasing Attacks on Misappropriated Distributed Observers via Decentralized $H_\infty$ synthesis

We develop a decentralized $H_\infty$ synthesis approach to detection of biasing misappropriation attacks on distributed observers. Its starting point is to equip the observer with an attack model which is then used in the design of attack detectors. A two-step design procedure is proposed. First, an initial centralized setup is carried out which enables each node to compute the parameters of its attack detector online in a decentralized manner, without interacting with other nodes. Each such detector is designed using the $H_\infty$ approach. Next, the attack detectors are embedded into the network, which allows them to detect misappropriated nodes from innovation in the network interconnections.