In this paper we consider the problem of controlling a limited number of target nodes of a network. Equivalently, we can see this problem as controlling the target variables of a structured system, where the state variables of the system are associated to the nodes of the network. We deal with this problem from a different point of view as compared to most recent literature. Indeed, instead of considering controllability in the Kalman sense, that is, as the ability to drive the target states to a desired value, we consider the stronger requirement of driving the target variables as time functions. The latter notion is called functional target controllability. We think that restricting the controllability requirement to a limited set of important variables justifies using a more accurate notion of controllability for these variables. Remarkably, the notion of functional controllability allows formulating very simple graphical conditions for target controllability in the spirit of the structural approach to controllability. The functional approach enables us, moreover, to determine the smallest set of steering nodes that need to be actuated to ensure target controllability, where these steering nodes are constrained to belong to a given set. We show that such a smallest set can be found in polynomial time. We are also able to classify the possible actuated variables in terms of their importance with respect to the functional target controllability problem.

中文翻译：

---

网络的功能目标可控性：结构特性和高效算法

在本文中，我们考虑控制网络中有限数量的目标节点的问题。等效地，我们可以将此问题视为控制结构化系统的目标变量，其中系统的状态变量与网络的节点相关联。与最近的文献相比，我们从不同的角度处理这个问题。实际上，我们没有考虑卡尔曼意义上的可控性，即作为将目标状态驱动到所需值的能力，而是考虑将目标变量驱动为时间函数的更强要求。后一个概念称为功能目标可控性。我们认为，将可控性要求限制在一组有限的重要变量上，证明对这些变量使用更准确的可控性概念是合理的。值得注意的是，功能可控性的概念允许本着可控性结构方法的精神为目标可控性制定非常简单的图形条件。此外，功能方法使我们能够确定需要被驱动以确保目标可控性的最小转向节点集，其中这些转向节点被限制为属于给定的集合。我们表明可以在多项式时间内找到这样一个最小的集合。我们还能够根据它们对功能目标可控性问题的重要性对可能的驱动变量进行分类。确定需要被驱动以确保目标可控性的最小转向节点集合，其中这些转向节点被约束为属于给定集合。我们表明可以在多项式时间内找到这样一个最小的集合。我们还能够根据它们对功能目标可控性问题的重要性对可能的驱动变量进行分类。确定需要被驱动以确保目标可控性的最小转向节点集合，其中这些转向节点被约束为属于给定集合。我们表明可以在多项式时间内找到这样一个最小的集合。我们还能够根据它们对功能目标可控性问题的重要性对可能的驱动变量进行分类。