  In this paper the robust cooperative output regulation problem for
multi-agent systems (MAS) with general heterodirectional hyperbolic PIDE-ODE
agents is considered. This setup also covers networks of ODEs with arbitrarily
long input and output delays. The output of the agents can be defined at all
boundaries, in-domain and may depend on the ODE state, while disturbances act
on the agents in-domain, at the boundaries, the output and the ODE. The
communication network is described by a constant digraph and if its Laplacian
is reducible, then heterogeneous agents are permitted also in the nominal case.
The solution is based on the cooperative internal model principle, which
requires to include a diffusively driven internal model in the controller. The
corresponding state feedback regulator design starts with a local backstepping
stabilization of the coupled hyperbolic PIDE-ODE systems. It is shown that the
remaining simultaneous stabilization of the MAS can be traced back to the
simultaneous stabilization of the finite-dimensional cooperative internal
model. Solvability conditions in terms of the network topology and the agents
transfer behavior are presented. The new design method is applied to the
formation control of a platoon of uncertain heavy ropes carrying loads to
verify its applicability. Simulations confirm the synchronization performance
achieved by the resulting networked controller.
