  Robust output tracking is addressed in this paper for a heat equation with
Neumann boundary conditions and anti-collocated boundary input and output. The
desired reference tracking is solved using the well-known flatness and Lyapunov
approaches. The reference profile is obtained by solving the motion planning
problem for the nominal plant. To robustify the closed-loop system in the
presence of the disturbances and uncertainties, it is then augmented with PI
feedback plus a discontinuous component responsible for rejecting matched
disturbances with \textit{a priori} known magnitude bounds. Such control law
only requires the information of the system at the same boundary as the control
input is located. The resulting dynamic controller globally exponentially
stabilizes the error dynamics while also attenuating the influence of
Lipschitz-in-time external disturbances and parameter uncertainties. For the
case when the motion planning is performed over the uncertain plant, an
exponential Input-to-State Stability is obtained, preserving the boundedness of
the tracking error norm. The proposed controller relies on a discontinuous term
that however passes through an integrator, thereby minimizing the chattering
effect in the plant dynamics. The performance of the closed-loop system, thus
designed, is illustrated in simulations under different kinds of reference
trajectories in the presence of external disturbances and parameter
uncertainties.
