State constraints are very common in actual networked systems. The main purpose of this article is to investigate the constrained set controllability of $k$-valued logical control networks (KVLCNs), the states of which are within a finite set. At first, the dynamics of KVLCNs with state constraints (SC-KVLCNs) can be equivalently written as an bilinear system by applying algebraic state space representation approach. After that, a method is presented to construct a kind of constrained set controllability matrix, based on which, a criterion is put forward to solve the constrained set controllability problem of KVLCNs. In addition, the constrained set controllability is applied to the partial stabilization, output tracking, output synchronization and observability of SC-KVLCNs. Finally, to implement the main results of this article, three examples are given.

状态约束在实际的网络系统中非常常见。本文的主要目的是研究约束集的可控性。$ķ$值逻辑控制网络（KVLCN），其状态在有限集中。首先，通过应用代数状态空间表示方法，可以将具有状态约束的KVLCN动力学（SC-KVLCN）等效地写为双线性系统。在此基础上，提出了一种构造约束集可控性矩阵的方法，并在此基础上提出了解决KVLCNs约束集可控性问题的准则。另外，约束集的可控制性被应用于SC-KVLCN的部分稳定，输出跟踪，输出同步和可观察性。最后，为实现本文的主要结果，给出了三个示例。