Optimal circadian rhythm control with light input for rapid entrainment and improved vigilance

Circadian rhythm is the biological process critical to the well being of all living organisms. The circadian rhythms oscillate with a period of approximately 24 hours due to the light-darkness pattern of the solar day. Circadian disruption, as experienced by night shift workers, travelers, submariners or miners, can lead to lower productivity, sleep disorder, and other more serious health problems. Using artificial light to regulate the circadian rhythm has long been proposed. The common approach is to use the phase response curve - the amount of steady state phase shift due to light pulses applied at specified times. In this paper, we consider a commonly used nonlinear second order oscillator model for the circadian rhythm response with light intensity as the input. Our first goal is to establish a performance bound by solving the minimum time control problem for a specified phase shift with contrained light intensity. The result is a much faster phase shift as compared to natural light-darkness pattern. We further extend the optimal control to vigilance, which is regulated in part by circadian rhythm, to maximize a vigilance lower bound for specified time and duration. Based on the two-process model of vigilance, the problem is formulated as an optimal control of switched system, and the optimization strategy is demonstrated via a simulation example.