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

  • Authors:

  • B. Pluymers;L. Roobrouck;J. Buijs;J. A. K. Suykens;B. De Moor

  • Affiliations:

  • Department of Electrical Engineering, Katholieke Universiteit Leuven, ESAT-SCD-SISTA, Kasteelpark Arenberg 10, B-3001 Heverlee (Leuven), Belgium;Department of Electrical Engineering, Katholieke Universiteit Leuven, ESAT-SCD-SISTA, Kasteelpark Arenberg 10, B-3001 Heverlee (Leuven), Belgium;Department of Electrical Engineering, Katholieke Universiteit Leuven, ESAT-SCD-SISTA, Kasteelpark Arenberg 10, B-3001 Heverlee (Leuven), Belgium;Department of Electrical Engineering, Katholieke Universiteit Leuven, ESAT-SCD-SISTA, Kasteelpark Arenberg 10, B-3001 Heverlee (Leuven), Belgium;Department of Electrical Engineering, Katholieke Universiteit Leuven, ESAT-SCD-SISTA, Kasteelpark Arenberg 10, B-3001 Heverlee (Leuven), Belgium

  • Venue:
  • Automatica (Journal of IFAC)
  • Year:
  • 2005

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Abstract

Recent papers (IEEE Transactions on Automatic Control 48(6) (2003) 1092-1096, Automatica 38 (2002) 1061-1068, Systems and Control Letters 48 (2003) 375-383) 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 without 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. 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 (IEEE Transactions on Automatic Control 48(6) (2003) 1092-1096, Automatica 38 (2002) 1061-1068). 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 an inverted pendulum.