Sparsity-Exploiting Anytime Algorithms for Model Predictive Control: A Relaxed Barrier Approach

We present and analyze a novel class of stabilizing and numerically efficient model predictive control (MPC) algorithms for discrete-time linear systems subject to polytopic input and state constraints. The proposed approach combines the previously presented concept of relaxed barrier function-based MPC with suitable warm-starting and sparsity-exploiting factorization techniques and allows to rigorously prove important stability and constraint satisfaction properties of the resulting closed-loop system independently of the number of performed Newton iterations. The effectiveness of the proposed approach is demonstrated by means of a numerical benchmark example.