  We propose a general method for optimizing periodic input waveforms for
global entrainment of weakly forced limit-cycle oscillators based on phase
reduction and nonlinear programming. We derive averaged phase dynamics from the
mathematical model of a limit-cycle oscillator driven by a weak periodic input
and optimize the Fourier coefficients of the input waveform to maximize
prescribed objective functions. In contrast to the optimization methods that
rely on the calculus of variations, the proposed method can be applied to a
wider class of optimization problems including global entrainment objectives.
As an illustration, we consider two optimization problems, one for achieving
fast global convergence of the oscillator to the entrained state and the other
for realizing prescribed global phase distributions in a population of
identical uncoupled noisy oscillators. We show that the proposed method can
successfully yield optimal input waveforms to realize the desired states in
both cases.
