PDE‐based containment control of linear multi‐agent systems

Abstract This contribution considers the containment control problem for linear multi‐agent systems (MAS) using continuum models in form of linear parabolic PDEs. For this, a networked controller is designed, that ensures the asymptotic convergence of finite‐dimensional agents into a containment area specified by dynamic leaders. This problem is traced back to an output regulation problem for a continuum model independent of the number of agents, which also takes disturbances into account. A prescribed formation is assigned for the MAS in the containment area by using Bézier curves. Using bilateral backstepping a tracking controller is designed, which allows to distribute the control effort between the two boundary agents. The states are estimated by an infinite‐dimensional disturbance observer. For this, both a folding observer with network communication and two boundary observers without network communication are introduced. A fully distributed solution of the containment control problem is obtained by employing a continuum signal model observer, which communicates the states of the leader and disturbance model to all agents. The desired communication topology is imposed after the design by a spatial discretization. A simulation example illustrates the effectiveness of the new method for the networked controller design.