Weight recentered barrier functions and smooth polytopic terminal set formulations for linear model predictive control

In the context of barrier function based model predictive control, a suitable recentering of the underlying barrier functions is essential for ensuring stability properties of the closed-loop system. We present a novel method for the recentering of logarithmic barrier functions which can be applied to a wide class of problems. In contrast to existing approaches, the recentering is achieved by a suitable weighting of the respective barrier functions and does not involve any gradient terms. In addition, a new approach towards the design of stabilizing barrier function based linear MPC formulations with polytopic terminal sets is presented which demonstrates possible benefits of the new recentering procedure.