Circadian rhythm is an important biological process for human as it modulates a wide range of physiological processes, including body temperature, sleep-wake cycle, and cognitive performance. As the most powerful external stimulus of circadian rhythm, light has been studied as an input to regulate the circadian phase and sleep. This paper addresses the human alertness optimization problem, by tuning lighting and sleep schedule, in cases of night-shift workers and subjects with certain mission periods based on dynamics of the circadian rhythm system. A new three-process hybrid dynamic model is proposed and used for simulating the circadian rhythm and predicting subjective alertness and sleepiness. We propose a controllable sleep schedule and consider it in the alertness optimization problem, which allows slightly delaying the sleep time and advancing the wake time instead of following the spontaneous sleep schedule constraints in original two-process model. Variational calculus is applied to evaluate the impacts of light and sleep schedules on the alertness and a gradient descent algorithm is proposed to determine the optimal solutions to maximize the alertness level in various cases. Numerical simulation results demonstrate that the neurobehavioral performance during certain periods can be significantly improved by optimizing the light input and sleep/wake times compared to empirical data.
Mathematics 10(11), 1916, Dynamical Systems Section, Special Issue on Control Problem of Nonlinear Systems with Applications, June 2022. https://doi.org/10.3390/math10111916