HYDRA

Complex networks in Air Force-relevant applications, including multi-vehicle control, energy systems, and neuronal networks, are expected to guarantee performance, stability, and availability. These networks are expected to be robust against natural failures and resilient against deliberate attacks. Two critical failure modes are (i) antagonistic interactions, in which an interaction between nodes causes their state values to separate, and (ii) interdependent failures, in which the failure of a single node or edge can trigger cascading failures of other nodes and edges. Agile response to such failures requires design of an efficient monitoring system that is integrated into the network. At present, there is no computationally tractable analytical framework for modeling and designing resilient networks with provable performance guarantees.

We propose to research and develop a submodular optimization framework for resilient complex networks. Submodularity is a diminishing returns property that enables the development of computationally efficient algorithms with provable optimality bounds. Based on our extensive prior work on submodularity in network dynamics and control, we believe that many of the key metrics quantifying network stability, performance, and resilience have a submodular structure.