Adaptive pinning control for the projective synchronization of drive-response dynamical networks

This paper studies the projective synchronization of a drive-response dynamical network of partially linear systems. The coupling-configuration matrix of the network is not necessarily symmetric. Two adaptive pinning control strategies are derived based on the Barbalat’s Lemma. In the first control strategy, the pinning control gain is adaptively updated to realize the projective synchronization. In the second control strategy, both the pinning control gain and the coupling strength between nodes are adaptively updated. Numerical simulation results show that the coupling strength needed in the second control strategy is smaller than that in the first control strategy to achieve the projective synchronization of the network.