  Reference governors are add-on schemes that are used to modify trajectories
to prevent controlled dynamical systems from violating constraints and so are
playing an increasingly important role in aerospace, robotic, and other
engineering applications. Here we present a novel reference governor design for
systems whose polynomial constraints depend on unknown bounded parameters. This
is a significant departure from earlier treatments of reference governors,
where the constraints were linear or known, because here we transfer the
uncertainties into the constraints instead of having them in the closed loop
dynamics, which greatly simplifies the task of determining future evolution of
the constraints. Unlike our earlier treatment of reference governors with
polynomial constraints, which transformed the constraints into linear ones that
depend on an augmented state of the system, here we transform the constraints
into linear ones that depend on both the system's state and uncertain
parameters. Convexity allows us to compute the maximal output admissible set
for an uncertain pre-stabilized linear system. We show that it is sufficient to
only consider the extreme values of the uncertain parameters when computing and
propagating the polynomial constraints. We illustrate our method using an
uncertain longitudinal dynamics for civilian aircraft, which is controlled
using a disturbance compensation method and needs to satisfy input and state
constraints, and where our reference governor method ensures that safety
constraints are always satisfied.
