Circadian phase entrainment via nonlinear model predictive control

A nonlinear model predictive control algorithm is developed to investigate the phase‐resetting properties of robust nonlinear biological oscillators; in particular, those of the circadian rhythm. This pacemaker is an autonomous biochemical oscillator with a free‐running period close to 24 h. Research in chronobiology indicates that light stimuli may delay or advance the phase of the oscillator, allowing it to synchronize physiological processes and entrain to the environment. In this paper, a closed‐loop optimal phase tracking control algorithm is developed and applied to a mammalian circadian model. The integration of MPC‐based light pulses, coupled with environmental light:dark cycles, allows the circadian system to recover phase differences within 1.5 days—a fraction of the natural open‐loop simulated mammalian recovery time. Accelerated phase entrainment may alleviate disorders caused by circadian rhythms that are out of phase with the environment, and improve performance. Copyright © 2007 John Wiley & Sons, Ltd.