Multiparametric Linear Programming with Applications to Control

Parametric programming has received a lot of attention in the control literature in the past few years because model predictive controllers (MPC) can be posed in a parametric framework and hence pre-solved offline, resulting in a significant decrease in on-line computation effort. 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.