Interpolation Based MPC for LPV Systems using Polyhedral Invariant Sets

Guaranteeing asymptotic stability and recursive constraint satisfaction for a set of initial states that is as large as possible and with both a minimal control cost and computational load can be identified as a common objective in the model predictive control (MPC) community. General interpolation (Rossiter et al., 2004, Bacic et al, 2003) provides a favourable trade oil between these different aspects, however, in the robust case, this requires on-line semi-definite programming (SDP), since one typically employs ellipsoidal invariant sets. Recently, (Pluymers et al., 2005) have proposed an efficient algorithm for constructing the robust polyhedral maximal admissible set (Gilbert et al., 1991) for linear systems with polytopic model uncertainty. In this paper a robust interpolation based MPC method is proposed that makes use of these sets. The algorithm is formulated as a quadratic program (QP) and is shown to have improved feasibility properties, efficiently cope with non-symmetrical constraints and give better control performance than existing interpolation based robust MPC algorithms.