Constrained linear MPC with time-varying terminal cost using convex combinations

Recent papers [3,4,16] have introduced dual-mode MPC algorithms using a time-varying terminal cost and/or constraint. The advantage of these methods is the enlargement of the admissible set of initial states whithout sacrificing local optimality of the controller, but this comes at the cost of a higher computational complexity. This paper delivers two main contributions in this area. First, a new MPC algorithm with a time-varying terminal cost and constraint is introduced. The algorithm uses convex combinations of off-line computed ellipsoidal terminal constraint sets and uses the associated cost as a terminal cost. In this way a significant on-line computational advantage is obtained. A new algorithm is proposed to off-line calculate these sets of the ellipsoidal terminal constraints. A further refinement of the on-line algorithm using sparse convex combinations and a reformulation using second-order cones (SOCs) are also discussed. The second main contribution is the introduction of a general stability theorem, proving stability of both the new MPC algorithm and several existing MPC schemes [3,4]. This allows a theoretical comparison to be made between the different algorithms. The new algorithm using convex combinations is illustrated and compared with other methods on the example of a copolymerization reactor and an inverted pendulum.