Interpolation based robust MPC with exact constraint handling

Recent papers (Bacic et al., 2003, Pluymers et al., 2005) have shown that interpolation between different fixed linear control laws can lead to control algorithms with large feasible regions and low on-line computational complexity. The feasible region was shown to be equal to the convex hull of the feasible regions of the different linear control laws between which the interpolation takes place. This paper extends the results of (Pluymers et al., 2005) and shows that the feasible region can be significantly enlarged beyond the convex hull by taking the interaction between the different control laws into account in the calculation of the feasible region. This paper deals with linear systems with polytopic uncertainty description and makes use of polyhedral invariant sets. Rigorous proofs of the results are provided.