Parameter Identification and Adaptive Control of Uncertain Goodwin Oscillator Networks with Disturbances

This paper investigates the dynamic properties of a differential equation model of mammals’ circadian rhythms, including parameter identification, adaptive control, and outer synchronization. The circadian oscillator network is described by a Goodwin oscillator network, the couplings of which are from vasoactive intestinal polypeptides described by modified Van der Pol oscillators. We build up a drive-response system consisting of two networks with unknown parameters and disturbances. Then, we propose effective parameter updating laws to identify the unknown parameters and design adaptive control strategies to achieve outer synchronization in the drive-response system. As special cases, two succinct corollaries are presented for different instances. All the theoretical results are proved through strict mathematical deduction based on Lyapunov stability theory, and a numerical example is also carried out to illustrate the effectiveness.