Invariant set constructions for feasible reference tracking

Model predictive control strategy is based on the iterative resolution of a constrained optimization problem. In this context, the feasibility represents a central issue. The present paper concentrates on the use of the invariant sets to guarantee the feasibility of the predictive control law for reference tracking applications. In a first stage, two basic algorithms to approximate the maximal invariant set (MPI) was presented. The first one proposes set iterations using a contraction procedure, while the second one uses an expansive construction. In a second stage, these procedures are adapted for the computation of feasible reference tracking (FRT) sets.