Brief paper: Decomposition principle in model predictive control for linear systems with bounded disturbances

  • Authors:

  • Dan Sui;Le Feng;Morten Hovd;Chong Jin Ong

  • Affiliations:

  • Department of Engineering Cybernetics, Norwegian University of Science and Technology 7491, Norway and Singapore-MIT Alliance, National University of Singapore, Singapore 119260, Singapore;Department of Engineering Cybernetics, Norwegian University of Science and Technology 7491, Norway;Department of Engineering Cybernetics, Norwegian University of Science and Technology 7491, Norway;Singapore-MIT Alliance, National University of Singapore, Singapore 119260, Singapore

  • Venue:
  • Automatica (Journal of IFAC)
  • Year:
  • 2009

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Abstract

Considering a constrained linear system with bounded disturbances, this paper proposes a novel approach which aims at enlarging the domain of attraction by combining a set-based MPC approach with a decomposition principle. The idea of the paper is to extend the ''pre-stabilizing'' MPC, where the MPC control sequence is parameterized as perturbations to a given pre-stabilizing feedback gain, to the case where the pre-stabilizing feedback law is given as the linear combination of a set of feedback gains. This procedure leads to a relatively large terminal set and consequently a large domain of attraction even when using short prediction horizons. As time evolves, by minimizing the nominal performance index, the resulting controller reaches the desired optimal controller with a good asymptotic performance. Compared to the standard ''pre-stabilizing'' MPC, it combines the advantages of having a flexible choice of feedback gains, a large domain of attraction and a good asymptotic behavior.