In order to guarantee stability, known results for MPC without additional
terminal costs or endpoint constraints often require rather large prediction
horizons. Still, stable behavior of closed loop solutions can often be observed
even for shorter horizons. Here, we make use of the recent observation that
stability can be guaranteed for smaller prediction horizons via Lyapunov
arguments if more than only the first control is implemented. Since such a
procedure may be harmful in terms of robustness, we derive conditions which
allow to increase the rate at which state measurements are used for feedback
while maintaining stability and desired performance specifications. Our main
contribution consists in developing two algorithms based on the deduced
conditions and a corresponding stability theorem which ensures asymptotic
stability for the MPC closed loop for significantly shorter prediction
horizons.Comment: 6 pages, 3 figure
