  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 large coupling gain is
applied to couple any pair of connected oscillators, the proposed method first
casts the whole 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 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.
