The primary concern of the present chapter is to address the distributed
leader-following consensus tracking problem for a network of agents governed by
uncertain diffusion PDEs with the Neumann-type boundary actuation and uncertain
spatially varying diffusivity. Except for the “leader” agent that generates the reference
profile to be tracked, all remaining agents, called “followers,” are required to
asymptotically track the infinite-dimensional time-varying leader state. The dynamics
of the follower agents are affected by smooth boundary disturbances unbounded
in magnitude and with a bounded derivative. The proposed local interaction rule is
developed by assuming that only neighboring collocated boundary sensing is available,
and it consists of a nonlinear sliding-mode-based protocol. The performance
and stability properties of the resulting infinite-dimensional networked system are
then formally studied by means of Lyapunov analysis. The analysis demonstrates the
global exponential stability of the resulting error boundary-value problem in a suitable
Sobolev space. The effectiveness of the developed control scheme is supported
by simulation results.