Online Data-Driven Control of Networks

Analysis and control of network systems largely rely on the availability of the network topology and the governing dynamics. In some cases, where the network dynamics and topology may not be available, researchers have relied on data-driven methods for the control of networks. A strict requirement of these methods is the collection of large amounts of persistently exciting data to enable control design. Moreover, these methods are largely restricted to linear systems and due to the open-loop nature of the control, lack robustness in the presence of external disturbances. In order to overcome these limitations, we present an online data-driven closed-loop control architecture for a nonlinear network system with unknown topology. Our method uses a novel ‘cut-and-rewire’ technique to assign a network topology that meets the desired control objectives while obviating the need for persistently exciting inputs and large open-loop offline data collection. We provide local asymptotic (exponential) stability guarantees for the closed-loop dynamics. We validate the results on a network of Kuramoto oscillators and achieve synchronization, phase balancing, and cluster formation when the underlying oscillator network topology is unknown and with noisy measurements.