  In Model Predictive Control (MPC) formulations of trajectory tracking
problems, infeasible reference trajectories and a-priori unknown constraints
can lead to cumbersome designs, aggressive tracking, and loss of recursive
feasibility. This is the case, for example, in trajectory tracking applications
for mobile systems in the presence of constraints which are not fully known
a-priori. In this paper, we propose a new framework called Model Predictive
Flexible trajectory Tracking Control (MPFTC), which relaxes the trajectory
tracking requirement. Additionally, we accommodate recursive feasibility in the
presence of a-priori unknown constraints, which might render the reference
trajectory infeasible. In the proposed framework, constraint satisfaction is
guaranteed at all times while the reference trajectory is tracked as good as
constraint satisfaction allows, thus simplifying the controller design and
reducing possibly aggressive tracking behavior. The proposed framework is
illustrated with three numerical examples.
