On the design of phase locked loop oscillatory neural networks: Mitigation of transmission delay effects

This paper introduces a novel design of phase locked loop (PLL) based oscillatory neural networks (ONNs) to mitigate the frequency clustering phenomenon caused by transmission delays in real systems. Theoretical analysis of the ONN reveals that transmission delays can produce frequency clustering that leads to synchronization and convergence failure. This paper describes the redesign of ONN dynamics and associated system-level architecture to achieve robustness. Specifically, we first demonstrate that using the phase information of zero-crossing points of inputs as the PLL error signal enables the ONN dynamical model to correctly synchronize under uniform transmission delays. A Type-II PLL based ONN architecture is shown via simulation to provide this property in hardware. Furthermore, to accommodate non-uniform transmission delays in hardware, a phase synchronization technique is proposed that is shown to provide the correct synchronization behavior.