Irredundant lattice representations of continuous piecewise affine functions

• Jun Xu ^[3] ; Ton J.J. van den Boom ^[1] ; Bart De Schutter ^[1] ; Shuning Wang ^[2]
  1. [1] Delft University of Technology

     Delft University of Technology

     Países Bajos

     
  2. [2] Tsinghua University

     Tsinghua University

     China

     
  3. [3] China University of Petroleum, Beijing

     China University of Petroleum, Beijing

     China

     

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• Localización: Automatica: A journal of IFAC the International Federation of Automatic Control, ISSN 0005-1098, Vol. 70, 2016, págs. 109-120
• Idioma: inglés
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• Resumen

  • In this paper, we revisit the full lattice representation of continuous piecewise affine (PWA) functions and give a formal proof of its representation ability. Based on this, we derive the irredundant lattice PWA representations through removal of redundant terms and literals. Necessary and sufficient conditions for irredundancy are proposed. Besides, we explain how to remove terms and literals in order to ensure irredundancy. An algorithm is given to obtain an irredundant lattice PWA representation. In the worked examples, the irredundant lattice PWA representations are used to express the optimal solution of explicit model predictive control problems, and the results turn out to be much more compact than those given by a state-of-the-art algorithm.