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Multiparametric Linear Programming with Applications to Control


C.N. Jones, M. Baric, M. Morari

European Journal of Control, vol. 13, no. 2-3, pp. 152-170

Parametric programming has received a lot of attention in the control literature in the past few years due to the fact that model predictive controllers (MPC) can be posed in a parametric framework and hence pre--solved offline resulting in a significant increase in online computation speed. In this paper we survey recent work on parametric linear programming (pLP) from the point of view of the control engineer. We identify three types of algorithms, two arising from standard convex hull paradigms and one from a geometric intuition, and classify all currently proposed methods under these headings. Through this classification, we identify a third standard convex hull approach that offers significant potential for approximation of pLPs for the purpose of control. We present the resulting algorithm, based on the beneath/beyond paradigm, that computes low--complexity approximate controllers that guarantee stability and feasibility. Finally, numerical examples are provided that demonstrate the relative merits of the surveyed methods on problems of interest to control engineers.


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% Autogenerated BibTeX entry
@Article { JonBar:2007:IFA_2699,
    author={C.N. Jones and M. Baric and M. Morari},
    title={{Multiparametric Linear Programming with Applications to
    journal={European Journal of Control},
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