Interpolation based MPC with exact constraint handling : the nominal case

Interpolation techniques are known to reduce computational complexity of MPC algorithms (Rossiter et al., 2004, Bacic et al., 2003). However, despite giving good feasible regions, there is nevertheless often some conservatism. This paper presents a new insight on general interpolation which reduces this conservatism and hence allows a substantial increase in feasible regions and therefore the potential of the approach. In particular it shows that the feasible region may be far larger than the convex hull of the underlying regions. Rigorous proofs of the results are also provided.