Abstract:

It was focused on the pinning control problem for a class of complex dynamic networks with linearly continuoustime coupled nodes. A new method for designing pinning controllers with stochastic pinning viewpoint is firstly proposed, which is referred to be stochastic pinning control. By adding such a controller to a fraction of nodes the stochastic stability of the entire complex networks can be guaranteed. It is claimed that the stochastic pinning control method without adding the selected nodes always could also stabilize the complex networks. By exploiting the robust method, sufficient condition is given for a kind of generally complex networks with coupling matrix changing to be another one, where the designed stochastic pinning controller is still available. Based on the established results, some results with the expectation of Bernouli variable uncertain and unknown are presented too. Finally, the correctness and effectiveness of the proposed methods is verified by a numerical example.

Key words: Complex networks, Stochastic pinning control, Stochastic stabilization, Robustness, Adaptive control

摘要： 主要研究一类具有连续线性耦合节点的复杂动态网络系统的牵制控制问题, 提出了一种基于随机变
量的随机牵制控制方法。通过对部分节点施加带有随机变量的状态反馈牵制控制器, 可以实现整个复杂网络系统
的稳定。可以看出, 虽然随机牵制方法不要求控制器一直作用在选定的节点上, 但同样能使得复杂网络系统稳定。
运用鲁棒思想首次讨论了系统耦合矩阵发生变化时所设计的随机牵制控制器的有效性问题, 给出了所设计控制器
仍然能保证系统的稳定性的充分条件。基于所得结果, 进一步讨论了所含随机变量的期望值含有不确定性和未知
时的牵制控制问题。最后通过数值仿真进一步验证了所提方法的正确性和有效性。

关键词: 复杂网络, 随机牵制控制, 随机稳定, 鲁棒性, 自适应控制