Event‐Triggered Affine Formation Control for Linear Multi‐Agent Systems via Complex‐Valued Laplacian

ABSTRACT In this paper, event‐triggered affine formation control for linear multi‐agent systems with a directed communication topology graph is addressed. The dynamics of each agent are described by complex‐valued differential equations. A distributed event‐triggered strategy for achieving global convergence and reaching the target affine formation is designed, which can effectively avoid continuous updates of the controller. Moreover, the control parameters in the control strategy are dependent on the information of the complex‐valued Laplacian, which avoid the use of global information. The results show that any desired affine formation can be achieved. Furthermore, the event‐triggering time sequence for any agent does not exhibit Zeno behavior. Finally, a numerical simulation example is presented to illustrate the effectiveness of the obtained theoretical results.