Robust Cooperative Output Regulation for a Network of Parabolic PDE Systems

This article considers the robust cooperative output regulation for a network of parabolic PDE systems. The solution to this problem is obtained by extending the cooperative internal model principle from finite to infinite dimensions. For a time-invariant digraph describing the communication topology, a two-step backstepping approach is presented to systematically design cooperative state feedback regulators. This allows to solve both the leader–follower and the leaderless output synchronization problem in the presence of disturbances and model uncertainty for a finite-dimensional leader. Solvability conditions of the robust cooperative output regulation problem are presented in terms of the communication graph and the agent transfer behavior. The results of this article are demonstrated for a network consisting of four uncertain parabolic agents with and without a finite-dimensional leader in the presence of disturbances.