  Motivated by engineering applications of subsea installation by deepwater
construction vessels in oil drilling, and of aid delivery by unmanned aerial
vehicles in disaster relief, we develop output-feedback boundary control of
heterodirectional coupled hyperbolic PDEs sandwiched between two ODEs, where
the measurement is the output state of one ODE and suffers a time delay. After
rewriting the time-delay dynamics as a transport PDE of which the left boundary
connects with the sandwiched system, a state observer is built to estimate the
states of the overall system of ODE-heterodirectional coupled hyperbolic
PDEs-ODE-transport PDE using the right boundary state of the last transport
PDE. An observer-based output-feedback controller acting at the first ODE is
designed to stabilize the overall system using backstepping transformations and
frequency-domain designs. The exponential stability results of the closed-loop
system, boundedness and exponential convergence of the control input are
proved. The obtained theoretical result is applied to control of a deepwater
oil drilling construction vessel as a simulation case, where the simulation
results show the proposed control design reduces cable oscillations and places
the oil drilling equipment to be installed in the target area on the sea floor.
Performance deterioration under extreme and unmodeled disturbances is also
illustrated.
