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Abstract Spontaneous synchronization is ubiquitous in natural and man-made systems. It underlies emergent behaviors such as neuronal response modulation and is fundamental to the coordination of robot swarms and autonomous vehicle fleets. Due to its simplicity and physical interpretability, pulse-coupled oscillators has emerged as one of the standard models for synchronization. However, existing analytical results for this model assume ideal conditions, including homogeneous oscillator frequencies and negligible coupling delays, as well as strict requirements on the initial phase distribution and the network topology. Using reinforcement learning, we obtain an optimal pulse-interaction mechanism (encoded in phase response function) that optimizes the probability of synchronization even in the presence of nonideal conditions. For small oscillator heterogeneities and propagation delays, we propose a heuristic formula for highly effective phase response functions that can be applied to general networks and unrestricted initial phase distributions. This allows us to bypass the need to relearn the phase response function for every new network. 

Phasor measurement units (PMUs) are playing an increasingly important role in wide-area monitoring and the control of power systems. PMUs allow synchronous real-time measurements of voltage, phase angle, and frequency from multiple remote locations in the grid, enabled by their ability to align to global positioning system (GPS) clocks. Given that this ability is vulnerable to GPS spoofing attacks, which have been confirmed easy to launch, in this paper, we propose a distributed real-time wide-area oscillation estimation approach that is robust to GPS spoofing on PMUs and their associated phasor data concentrators. The approach employs the idea of checking update consistency with histories and across distributed nodes and can tolerate up to one third of compromised nodes. It can be implemented in a completely decentralized architecture and in a completely asynchronous way. The effectiveness of the approach is confirmed by numerical simulations of the IEEE 68-bus power system models.