Time-Optimal Control for Circadian Entrainment for a Model with Circadian and Sleep Dynamics

In this paper, we study an optimal control problem for circadian rhythm regulation. The objective of the problem is to find a lighting schedule that minimizes the time required for a subject’s circadian rhythm to synchronize with a reference circadian rhythm. We previously solved this problem with a bang-off control algorithm. However, this existing solution neglects the sleep dynamics and often results in an unreasonably uncomfortable schedule (with excessive sleepiness). In this paper, we use a hybrid system model that contains both the circadian and sleep dynamics. Using variational analysis, we show that the time-optimal control problem is still a bang-off control algorithm, but from a class of algorithms that is richer than the one previously reported.