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Controller Complexity Reduction for Piecewise Affine Systems Through Safe Region Elimination


F.J. Christophersen, M.N. Zeilinger, C.N. Jones, M. Morari

IEEE Conference on Decision and Control, New Orleans, USA

We consider the class of piecewise affine optimal state feedback control laws applied to discrete-time piecewise affine systems, motivated by recent work on the computation of closed-form MPC controllers. The storage demand and complexity of these optimal closed-form solutions limit their applicability in most real-life situations. In this paper we present a novel algorithm to a posteriori reduce the storage demand and complexity of the closed-form controller without losing closed-loop stability or all time feasibility while guaranteeing a bounded performance decay compared to the optimal solution. The algorithm combines simple polyhedral manipulations with (multi-parametric) linear programming and the effectiveness of the algorithm is demonstrated on a large numerical example.


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M. Morari

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  author       = {F. J. Christophersen and M. N. Zeilinger and
                  C. N. Jones and M. Morari},
  title	       = {{Controller Complexity Reduction for Piecewise
                  Affine Systems Through Safe Region Elimination}},
  booktitle    = {Proc.~of the Conf.~on Decision \& Control},
  year	       = 2007,
  address      = {New Orleans, USA},
  month	       = dec,
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