非线性复杂网络的结构平衡自适应跟踪控制

Adaptive Tracking Control for Nonlinear Complex Dynamic Network to Structural Balance

从大系统的角度,复杂动态网络可视为由节点子系统与连接关系子系统耦合而成。主要关注非线性连接关系动态子系统的跟踪控制问题,研究如何使非线性复杂动态网络达到结构平衡状态。采用Riccati矩阵微分方程对网络连接关系子系统进行建模,并设计合适的自适应控制器使系统渐近跟踪上一个给定的结构平衡矩阵。数值仿真验证了该控制器的有效性,表明在控制器的作用下,网络表现出结构平衡的特征。

From the perspective of large-scale system,a complex dynamical network can be regarded to be composed of the nodes subsystem and links subsystem which are mutually coupled. This paper focuses on the tracking control for nonlinear dynamic links subsystems. The research purpose is to understand how to drive the nonlinear complex dynamical network to structural balance. A Riccati matrix differential equation is used to model the continuous time-varying nonlinear links subsystem. Then,a suitable adaptive controller is designed to make the links subsystem track a given structural balance matrix asymptotically. Numerical simulation experiments prove the effectiveness of the controller design. In other words,by the effect of the controller,the network reaches the state of structural balance.