Phase resetting control based on direct phase response curve

The problem of controlled phase adjustment (resetting) for models of biological oscillators is considered. The proposed approach is based on oscillators excitation by a pulse, that results in the phase advancement or delay. Design procedure is presented for a series of pulses generation ensuring the required phase resetting. The solution is based on the direct phase response curve (PRC) approach. The notion of direct PRC is developed and non-local PRC model is proposed for oscillators. This model is more suitable for phase dynamics description under inputs excitation with sufficiently high amplitudes. The proposed model is used for controls design. Two control strategies are tested, the open-loop control (that generates a predefined table of instants of the pulses activation ensuring the resetting) and the feedback control (that utilizes information about the current phase value measured once per pulse application). The open-loop control is easier for implementation, the feedback control needs the estimation of the actual phase in the oscillating system. The algorithm of phase estimation is also presented. The conditions of the model and the controls validity and accuracy are determined. Performance of the obtained solution is demonstrated via computer simulation for two models of circadian oscillations and a model of heart muscle contraction. It is shown that in the absence of disturbances the open-loop and the feedback controls have similar performance. Additionally, the feedback control is insensitive to external disturbances influence. In these examples the presented scheme for phase values estimation demonstrates better accuracy than the conventional one.