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.

本文研究了动力学未知的多维复杂网络的投影同步问题。首先，通过选择一个投影矩阵，得到误差系统，并提出了一种基于事件的投影同步控制策略，以实现两个不同维数的复杂网络之间的投影同步。结果表明，射影同步问题可以转化为具有性能函数的误差系统的最优调节。然后，提出了一种数据驱动控制方案来实现事件触发的投影同步控制策略，该策略由标识符，注释网络和执行器组成。该标识符用于估计未知动态。使用执行器来构造控制输入，并通过评论家网络估计最佳值。致动器和批评者网络均基于神经网络。神经网络权重和控制器在事件触发的瞬间进行更新，从而可以节省计算和通信资源。通过采用适当的事件触发阈值和神经网络的学习率，证明同步误差渐近逼近零，并且排除了芝诺行为。最后，通过数值例子验证了所获得结果的有效性。通过采用适当的事件触发阈值和神经网络的学习率，证明同步误差渐近逼近零，并且排除了芝诺行为。最后，通过数值例子验证了所获得结果的有效性。通过采用适当的事件触发阈值和神经网络的学习率，证明同步误差渐近逼近零，并且排除了芝诺行为。最后，通过数值例子验证了所获得结果的有效性。