We analyze the robust stability properties of iteration schemes for the algorithmic implementation of model predictive control for linear discrete-time systems. The underlying optimization employs a relaxed barrier function based problem formulation and performs only a limited, possibly arbitrarily small, number of optimization algorithm iterations per sampling instant. Based on the input-to-state stability concept, the resulting overall closed-loop system consisting of system state and optimizer dynamics is shown to be robustly stable with respect to both external and internal disturbances. Implications for the case of certainty equivalence output feedback as well as possible extensions are also discussed.
['Christian Feller', 'Christian Ebenbauer']
Robust stability properties of MPC iteration schemes based on relaxed barrier functions