  This work proposes a finite-horizon optimal control strategy to solve the
tracking problem while providing avoidance features to the closed-loop system.
Inspired by the set-point tracking model predictive control (MPC) framework,
the central idea of including artificial variables into the optimal control
problem is considered. This approach allows us to add avoidance features into
the set-point tracking MPC strategy without losing the properties of an
enlarged domain of attraction and feasibility insurances in the face of any
changing reference. Besides, the artificial variables are considered together
with an avoidance cost functional to establish the basis of the strategy,
maintaining the recursive feasibility property in the presence of a previously
unknown number of regions to be avoided. It is shown that the closed-loop
system is recursively feasible and input-to-state-stable under the mild
assumption that the avoidance cost is uniformly bounded over time. Finally, two
numerical examples illustrate the controller behavior.
