For partially interdependent networks composed of two subnetworks, the finite‐time optimal pinning control problem is investigated. Among them, only a part of the nodes between the two subnetworks are interdependent on each other. In the network, the coupling relationship between any two nodes of the network is a continuous nonlinear function. Based on the pinning control, the optimal control theory, Kalman's controllability rank conditions, and introducing the Lagrange function and applying controllers to the partial nodes of the network, we propose some characterization indicators which ensure that the two subnetworks of partially interdependent networks can synchronize to the equilibrium points of their isolate systems, separately. Finally, some numerical simulations are performed on the partially interdependent networks including two small world subnetworks. The results show that the optimal pinning control method proposed in this article can greatly reduce the control costs and achieve the ideal synchronous status quickly.

中文翻译：

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部分相互依赖的网络的有限时间最佳钉扎控制和同步

对于由两个子网组成的部分相互依赖的网络，研究了有限时间最优钉扎控制问题。其中，两个子网之间只有一部分节点相互依赖。在网络中，网络中任意两个节点之间的耦合关系是一个连续的非线性函数。基于钉扎控制，最优控制理论，卡尔曼可控性秩条件，并引入拉格朗日函数并将控制器应用于网络的部分节点，我们提出了一些表征指标，以确保部分相互依赖的网络的两个子网可以同步到各自隔离系统的平衡点。最后，在包括两个小世界子网络的部分相互依赖的网络上执行了一些数值模拟。结果表明，本文提出的最优钉扎控制方法可以大大降低控制成本，并迅速达到理想的同步状态。