Reduced Parameterisation MPC for input-constrained unstable linear systems: part 2: properties

This paper presents the properties of a new variant of model predictive control called Reduced Parameterisation Model Predictive Control (RPMPC). The new algorithm uses the structure of the null controllable set of input constrained unstable systems to produce a closed-loop system with a region of attraction that is an arbitrarily close approximation to this set. We show that the RPMPC algorithm converges in a finite number of iterations and we establish stability of the resulting closed-loop system. In addition, we present a rigorous worst case complexity analysis together with average computational tests. Both these studies show that for long horizons RPMPC has a lower computational requirement than that of standard MPC.