  Adaptive safe control employing conventional continuous infinite-time
adaptation requires that the initial conditions be restricted to a subset of
the safe set due to parametric uncertainty, where the safe set is shrunk in
inverse proportion to the adaptation gain. The recent regulation-triggered
adaptive control approach with batch least-squares identification (BaLSI,
pronounced "ballsy") completes perfect parameter identification in finite time
and offers a previously unforeseen advantage in adaptive safe control, which we
elucidate in this paper. Since the true challenge of safe control is exhibited
for CBF of a high relative degree, we undertake a safe BaLSI design in this
paper for a class of systems that possess a particularly extreme relative
degree: ODE-PDE-ODE sandwich systems. Such sandwich systems arise in various
applications, including delivery UAVs (Unmanned Aerial Vehicles) with a
cable-suspended load. Collision avoidance of the payload with the surrounding
environment is required. The considered class of plants is $2\times2$
hyperbolic PDEs sandwiched by a strict-feedback nonlinear ODE and a linear ODE,
where the unknown coefficients, whose bounds are known and arbitrary, are
associated with the PDE in-domain coupling terms that can cause instability and
with the input signal of the distal ODE. This is the first safe adaptive
control design for PDEs, where we introduce the concept of PDE CBF whose
non-negativity, as well as the ODE CBF's non-negativity, are ensured with a
backstepping-based safety filter. Our safe adaptive controller is explicit and
operates in the entire original safe set.
