  The light-based minimum-time circadian entrainment problem for mammals,
Neurospora, and Drosophila is studied based on the mathematical models of their
circadian gene regulation. These models contain high order nonlinear
differential equations. Two model simplification methods are applied to these
high-order models: the phase response curves (PRC) and the Principal Orthogonal
Decomposition (POD). The variational calculus and a gradient descent algorithm
are applied for solving the optimal light input in the high-order models. As
the results of the gradient descent algorithm rely heavily on the initial
guesses, we use the optimal control of the PRC and the simplified model to
initialize the gradient descent algorithm. In this paper, we present: (1) the
application of PRC and direct shooting algorithm on high-order nonlinear
models; (2) a general process for solving the minimum-time optimal control
problem on high-order models; (3) the impacts of minimum-time optimal light on
circadian gene transcription and protein synthesis.
