The human circadian rhythm evolved as a mechanism by which living beings can synchronize their biological processes with the light and dark pattern of the terrestrial day. The circadian rhythm effectively functions as a master clock that regulates these processes. In humans, the circadian rhythm is tightly linked to various physiological processes, such as sleep, metabolism, and neuro-behavioral processes.  Disruption of the circadian rhythm is known to have negative impacts on health, ranging from fatigue in travelers with jetlag to an increased risk of cardiac disease and cancer in rotating shift workers. Furthermore, misalignment of the circadian phase and related neurobehavioral states (such as alertness) with the timing of critical tasks may lead to lower performance and higher risk of failure.

The sleep process in humans is very tightly connected to the circadian rhythm. The sleep drive, for example, is known to be modulated by the circadian rhythm. Sleep is critical to health, as it allows the body to recuperate and regenerate cells. It is also tied to neurocognitive performance; the lack of or mistiming of sleep have been empirically linked to degeneration of neurocognitive performance [8, 9] and disruption of circadian rhythm regulation.

Many Department of Defense (DoD) missions necessarily disrupt natural circadian cycles and sleep. For example, airlift and tanker missions can impair reaction times, lower attention spans, diminish memory recall, and increase human errors and elevate risk. Sleep duration is also found to affect cognitive performance. Other research has shown that sleep cycle disruption may be more of a contributing cause than a symptom of PTSD experience in veterans. Additionally, re- search conducted by the U.S. Naval Submarine Medical Research Laboratory, concludes that special operations forces may be able to phase-lock their circadian rhythms when traveling across time zones, via judicious control of light exposure.  In the circadian rhythm research literature, several mathematical models have been developed to capture the dynamics of circadian rhythm and sleep. These models are typically formulated to match experimental results from human subject studies. These models allow us to make quantitative predictions about, for example, the impact of lighting to a subject’s circadian rhythm, or the effects of circadian rhythm and sleep scheduling on a subject’s neurobehavioral states, such as alertness. The models typically incorporate some parameters, such as the free-running period of the subject’s circadian rhythm, which may be adapted to individual subjects, leading to personalized circadian and sleep health solutions. In this article, we present a novel approach to mathematically modeling circadian rhythm and sleep activity, and use the models to control environmental lighting and sleep schedule to enable optimal performance.