Brief An algorithm for multi-parametric quadratic programming and explicit MPC solutions

  • Authors:

  • Petter TøNdel;Tor Arne Johansen;Alberto Bemporad

  • Affiliations:

  • Department of Engineering Cybernetics, Norwegian University of Science and Technology, 7491 Trondheim, Norway;Department of Engineering Cybernetics, Norwegian University of Science and Technology, 7491 Trondheim, Norway;Dipartimento di Ingegneria dell'Informazione, University of Siena, 53100 Siena, Italy

  • Venue:
  • Automatica (Journal of IFAC)
  • Year:
  • 2003

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Abstract

Explicit solutions to constrained linear model predictive control problems can be obtained by solving multi-parametric quadratic programs (mp-QP) where the parameters are the components of the state vector. We study the properties of the polyhedral partition of the state space induced by the multi-parametric piecewise affine solution and propose a new mp-QP solver. Compared to existing algorithms, our approach adopts a different exploration strategy for subdividing the parameter space, avoiding unnecessary partitioning and QP problem solving, with a significant improvement of efficiency.