  Switched-actuator systems with setup times (SAcSSs) are systems in which the
actuator configuration has to be switched during operation, and where the
switching induces non-negligible actuator downtime. Optimally controlling
SAcSSs requires the online solving of both a discrete actuator allocation
problem, in which the switch-induced actuator downtime is taken into account,
as well as an optimization problem for the (typically continuous) control
inputs. Mixed-integer model predictive control (MI-MPC) offers a powerful
framework for tackling such problems. However, the efficient modeling of SAcSSs
for MI-MPC is not straightforward, and real-time feasibility is often a major
hurdle in practice. It is the objective of this paper to provide an intuitive
and systematic modeling procedure tailored to SAcSSs, which is specifically
designed to allow for user-friendly controller synthesis, and to yield
efficient MI-MPCs. We apply these new results in a case study of large-volume
magnetic-resonance-guided high-intensity focused ultrasound hyperthermia, which
involves the heating of tumors (using real-valued local heating controls, as
well as discrete range-extending actuator relocation during which no heating is
allowed) to enhance the efficacy of radio- and chemotherapy.
