2017/10/02 by Marcello Colombino, Dominic Groß, Colombino, Marcello +5 · 4 citations
Computer Science · Engineering · Physics and Astronomy · #Chaos control and synchronization #FOS: Mathematics #Nonlinear Dynamics and Pattern Formation #Optimization and Control (math.OC) #Stability and Controllability of Differential Equations
paper · pdf · doi:10.48550/arxiv.1710.00694
openalex publication_date 2017/10/02 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this work, we explore a new approach to synchronization of coupled\noscillators. In contrast to the celebrated Kuramoto model we do not work in\npolar coordinates and do not consider oscillations of fixed magnitude. We\npropose a synchronizing feedback based on relative state information and local\nmeasurements that induces consensus-like dynamics. We show that, under a mild\nstability condition, the combination of the synchronizing feedback with a\ndecentralized magnitude control law renders the oscillators' almost globally\nasymptotically stable with respect to set-points for the phase shift,\nfrequency, and magnitude. We apply these result to rigorously solve an open\nproblem in control of inverter-based AC power systems. In this context, the\nproposed control strategy can be implemented using purely local information,\ninduces a grid-forming behavior, and ensures that a network of AC power\ninverters is almost globally asymptotically stable with respect to a\npre-specified solution of the AC power-flow equations. Moreover, we show that\nthe controller exhibits a droop-like behavior around the standard operating\npoint thus making it backward-compatible with the existing power system\noperation.\n