Consensus Computation in Unreliable Networks: A System Theoretic Approach

This work addresses the problem of ensuring trustworthy computation in a linear consensus network. A solution to this problem is relevant for several tasks in multi-agent systems including motion coordination, clock synchronization, and cooperative estimation. In a linear consensus network, we allow for the presence of misbehaving agents, whose behavior deviate from the nominal consensus evolution. We model misbehaviors as unknown and unmeasurable inputs affecting the network, and we cast the misbehavior detection and identification problem into an unknown-input system theoretic framework. We consider two extreme cases of misbehaving agents, namely faulty (non-colluding) and malicious (Byzantine) agents. First, we characterize the set of inputs that allow misbehaving agents to affect the consensus network while remaining undetected and/or unidentified from certain observing agents. Second, we provide worst-case bounds for the number of concurrent faulty or malicious agents that can be detected and identified. Precisely, the consensus network needs to be 2k+1 (resp. k+1) connected for k malicious (resp. faulty) agents to be generically detectable and identifiable by every well behaving agent. Third, we quantify the effect of undetectable inputs on the final consensus value. Fourth, we design three algorithms to detect and identify misbehaving agents. The first and the second algorithm apply fault detection techniques, and affords complete detection and identification if global knowledge of the network is available to each agent, at a high computational cost. The third algorithm is designed to exploit the presence in the network of weakly interconnected subparts, and provides local detection and identification of misbehaving agents whose behavior deviates more than a threshold, which is quantified in terms of the interconnection structure

On the genericity properties in networked estimation: Topology design and sensor placement

In this paper, we consider networked estimation of linear, discrete-time dynamical systems monitored by a network of agents. In order to minimize the power requirement at the (possibly, battery-operated) agents, we require that the agents can exchange information with their neighbors only \emph{once per dynamical system time-step}; in contrast to consensus-based estimation where the agents exchange information until they reach a consensus. It can be verified that with this restriction on information exchange, measurement fusion alone results in an unbounded estimation error at every such agent that does not have an observable set of measurements in its neighborhood. To over come this challenge, state-estimate fusion has been proposed to recover the system observability. However, we show that adding state-estimate fusion may not recover observability when the system matrix is structured-rank ($S$-rank) deficient. In this context, we characterize the state-estimate fusion and measurement fusion under both full $S$-rank and $S$-rank deficient system matrices.Comment: submitted for IEEE journal publicatio