Date of Award
Doctor of Philosophy (PhD)
Electrical and Computer Engineering (Holcomb Dept. of)
Dr. Yongqiang Wang
Dr. Richard Groff
Dr. Ian D. Walker
Dr. Umesh Vaidya
In this dissertation, we consider the application of pulse-coupled oscillator theory to real-world, physical networks. When the phase of an oscillator is associated with a physical measure, such as clock timing or robotic heading, discontinuous adjustments of the oscillator's phase is undesirable and potentially disadvantageous. Rather, continuous adjustment of the oscillator phase value is needed over a certain amount of time. To ensure that both synchronization and desynchronization can still be achieved under the constraint of continuous phase value changes, we pursue a novel approach to analyze the generalization of a pulse-coupled oscillator network with a time-varying coupling strength. We provide rigorous mathematical proof for both pulse-coupled synchronization and desynchronization under the proposed phase continuity methods. We then correlate the continuous phase change of the oscillator to a specifically time-varying coupling strength of the network. To verify the analysis, we provide both simulated and experimental results for various synchronization and desynchronization algorithms using the proposed phase continuity methods.
Additionally, an oscillator may need to adjust its phase response to received pulses from connected neighbors in the network due to non-ideal conditions of physical systems, such as pulse propagation delay, non-identical oscillator frequencies, and general network topologies, once the network has been deployed. Direct analysis of pulse-coupled oscillator networks under non-ideal conditions is difficult, so we consider a novel approach of using reinforcement learning techniques to have the oscillators use their own experience to approximate an optimal phase response. Using appropriate measures to have a single oscillator estimate the state of the rest of the network, we determine a novel phase response function model in terms of the network topology. The optimality of the proposed phase response function is verified with simulated comparisons to existing synchronization algorithms.
Anglea, Timothy, "Pulse-Coupled Oscillator Networks: Achieving Phase Continuity and Learning Optimal Control in Physical Systems" (2022). All Dissertations. 3063.
Author ORCID Identifier