  This paper considers the design of finite control set model predictive
control (FCS-MPC) for discrete-time switched affine systems. Existing FCS-MPC
methods typically pursue practical stability guarantees, which ensure
convergence to a bounded invariant set that contains a desired steady state. As
such, current FCS-MPC methods result in unpredictable steady-state behavior due
to arbitrary switching among the available finite control inputs. Motivated by
this, we present a FCS-MPC design that aims to stabilize a steady-state limit
cycle compatible with a desired output reference via a suitable cost function.
We provide conditions in terms of periodic terminal costs and finite control
set control laws that guarantee asymptotic stability of the developed limit
cycle FCS-MPC algorithm. Moreover, we develop conditions for recursive
feasibility of limit cycle FCS-MPC in terms of periodic terminal sets and we
provide systematic methods for computing ellipsoidal and polytopic periodically
invariant sets that contain a desired steady-state limit cycle. Compared to
existing periodic terminal ingredients for tracking MPC with a continuous
control set, we design and compute terminal ingredients using a finite control
set. The developed methodology is validated on switched systems and power
electronics benchmark examples.
