  This paper is concerned with the cooperative output regulation problem for a
network of agents with different dynamics described by parabolic PDEs subject
to spatially- and time-varying parameters. Firstly, a networked controller is
designed achieving output synchronization for identical finite-dimensional
reference models, which deliver the state of the global reference model
required for the synchronization to the parabolic agents. The latter can be
subject to local disturbances acting in-domain, on all boundaries and on the
anti-collocated output to be controlled. The cooperative output regulation
problem is solved by designing local output feedback regulators for the
parabolic agents. This requires the solution of time-varying regulator
equations and the design of disturbance observers for parabolic systems with
spatially- and time-varying coefficients. For this, a systematic backstepping
approach is provided and it is shown that cooperative output regulation with
exponential convergence is ensured for the resulting multi-agent system. The
results of the paper are applied to the cooperative output regulation of a
heterogeneous network of four parabolic agents in the presence of local
disturbances.
