On Optimal Synchronization of Diffusively Coupled Heterogeneous Van der Pol Oscillators*

Abstract

This paper proposes a novel method to achieve and preserve synchronization for a set of connected heterogeneous Van der Pol oscillators. Unlike the state-of-the-art synchronization methods, in which a constant and large coupling gain is applied to couple any pair of connected oscillators, the proposed method first divides the synchronization process into two phases. The first one considers the period from the beginning to the first instant of synchronization, while the second phase covers the following time in which synchronization must be preserved. It is shown that a large coupling gain is adopted for the first phase, while the averaged coupling gain to practically preserve the synchronization in the second phase can be reduced significantly by using an offline optimized coupling law. Efficiency and performance of this method are confirmed by a set of numerical tests with different graphs and system dynamics.