A Method for Obtaining Continuous Solutions to Multiparametric Linear Programs

Authors:	Spjøtvold Jørgen, Norwegian University of Science and Technology, Norway Tøndel Petter, Norwegian University of Science and Technology, Norway Johansen Tor Arne, Norwegian University of Science and Technology, Norway
Topic:	2.4 Optimal Control
Session:	Control Applications of Optimization
Keywords:	Multiparametric programming, constrained optimal control, linearprogramming, quadratic programming, explicit model predictivecontrol.

Abstract

A modification of the geometric algorithm for solvingmultiparametric linear programs (mp-LP) is presented. Themodification preserves the simplicity of the algorithm and ensuresthat the optimal, piecewise affine, mapping from parameter tosolution space is continuous. When the mp-LP has non-uniquesolutions, the optimizer with the least Euclidian norm isselected.