Event-Based Projective Synchronization for Different Dimensional Complex Dynamical Networks with Unknown Dynamics by Using Data-Driven Scheme

In this paper, the projective synchronization problem for different dimensional complex networks (CNs) with unknown dynamics is investigated. First, by selecting a projective matrix, the error system is obtained and an event-based projective synchronization control policy is proposed to realize the projective synchronization between two complex networks with different dimensions. It is revealed that the projective synchronization problem can be transformed into the optimal regulation of the error system with a performance function. Then, a data-driven control scheme is proposed to implement the event-trigged projective synchronization control policy, which is composed of identifier, critic network and actuator. The identifier is applied to estimate the unknown dynamics. The actuator is employed to construct the control inputs and the optimal value is estimated by the critic network. Both actuator and critic network are based on neural networks. The neural network weights and controller are updated at event-triggered instant so that the computing and communication resources can be saved. By employing appropriate event-triggered threshold and learning rate of neural network, the synchronization error is proved to be be asymptotically approaching zero and the Zeno behaviors are excluded. Finally, a numerical example is given to verify the effectiveness of the obtained results.