  Given the high dimensionality and underlying complexity of many oscillatory
dynamical systems, phase reduction is often an imperative first step in control
applications where oscillation timing and entrainment are of interest.
Unfortunately, most phase reduction frameworks place restrictive limitations on
the magnitude of allowable inputs, limiting the practical utility of the
resulting phase reduced models in many situations. In this work, motivated by
the search for control strategies to hasten recovery from jet-lag caused by
rapid travel through multiple time zones, the efficacy of the recently
developed adaptive phase-amplitude reduction is considered for manipulating
oscillation timing in the presence of a large magnitude entraining stimulus.
The adaptive phase-amplitude reduced equations allow for a numerically
tractable optimal control formulation and the associated optimal stimuli
significantly outperform those resulting from from previously proposed optimal
control formulations. Additionally, a data-driven technique to identify the
necessary terms of the adaptive phase-amplitude reduction is proposed and
validated using a model describing the aggregate oscillations of a large
population of coupled limit cycle oscillators. Such data-driven model reduction
algorithms are essential in situations where the underlying model equations are
either unreliable or unavailable.
