Figure 10:

Demonstration of MPC for phase resetting in response to a weeklong rotating shift work schedule, described in [43]. This scenario involves 8h phase delays every two days when rotating from morning (06:00–14:00), to evening (14:00–22:00) to night (22:00–06:00) shifts, followed by days off. (A) Phase of oscillator under MPC compared to reference phase for the shift work problem. In this example, time corresponds to clock time, such that Per expression in an individual entrained for morning work will occur near dusk. The reference phase was adjusted to the next rotating shift following the last work cycle of the prior rotating shift. For this problem, τ = 2h and N_p = 5. (B) Timing of control inputs and ipPRC throughout the simulation. Because all shifts are achieved by delays, a slower sampling rate (longer duration between dosage changes) would have a similar efficacy. For simplicity, no light input to the clock was assumed in this case, though it may be incorporated as an additional disturbance input to the phase model, or applied as part of multi-input control.