In this study, the finite-time formation control of multi-agent systems with region constraints is studied. Multiple agents have first-order dynamics and a common target area. A novel control algorithm is proposed using local information and interaction. If the communication graph is undirected and connected and the desired framework is rigid, it is proved that the controller can be used to solve the formation problem with a target area. That is, all agents can enter the desired region in finite time while reaching and maintaining the desired formation shapes. Finally, a numerical example is given to illustrate the results.

In this paper, we address the problems of enumerating siphons and minimal siphons in ordinary Petri nets (PNs) by resorting to the semi-tensor product (STP) of matrices. First, a matrix equation, called the siphon equation (SE), is established by using STP. Second, an algorithm is proposed to calculate all siphons in ordinary PNs. An example is presented to illustrate the theoretical results and show that the proposed method is more effective than other existing methods in calculating all siphons of PNs. Third, an efficient recursion algorithm is also proposed, which can be applied to computing all minimal siphons for any ordinary PNs. Last, some results on the computational complexity of the proposed algorithms, in this paper, are provided, as well as experimental results.