NDLI: Optimized decision trees for point location in polytopic data sets

Content Provider	IEEE Xplore Digital Library
Author	Fuchs, A.N. Jones, C.N. Morari, M.
Copyright Year	2010
Description	Author affiliation: ETH Zurich, Zurich, Switzerland (Fuchs, A.N.; Jones, C.N.; Morari, M.)
Abstract	Explicit Model Predictive Control (EMPC) produces control laws defined over a set of polytopic regions in the state space. In this paper we present a method to create a binary search tree for point location in such polytopic sets, in order to provide a fast lookup of the control law corresponding to a given state. We use hyperplanes as decision criteria that are, contrary to previous works, not constrained to the boundaries of the polytopes. Each hyperplane is the solution of a mixed-integer optimization problem with two objectives: having the same number of polytopes on either side of the hyperplane and minimizing the number of polytopes cut by the hyperplane. Contrary to previous approaches, the method can be applied to polytopic sets where the polytopes are either adjacent with common facets (for classical EMPC) or separated in space (for suboptimal EMPC). There are two benefits using this approach: First, the method optimizes the balance of the tree. If a tree of the theoretically lowest possible depth (i.e. $log_{2}$ depth) exists, the algorithm will find it, although the time to solve the optimization problem may become prohibitive for large problems. Second, the method provides an efficient evaluation of suboptimal EMPC policies since it allows to maximize the distance of the hyperplane to the closest polytope that is not intersected.
Starting Page	5507
Ending Page	5512
File Size	731811
Page Count	6
File Format	PDF
ISBN	9781424474264
ISSN	07431619
e-ISBN	9781424474271
DOI	10.1109/ACC.2010.5530979
Language	English
Publisher	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Publisher Date	2010-06-30
Publisher Place	USA
Access Restriction	Subscribed
Rights Holder	American Automatic Control Council(AACC)
Subject Keyword	Decision trees Optimal control State-space methods Binary search trees Predictive models Predictive control Optimization methods Linear systems Cost function Robust control
Content Type	Text
Resource Type	Article
Subject	Electrical and Electronic Engineering

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4	Project PI / Joint PI	Principal Investigator and Joint Principal Investigators of the project	Dr. B. Sutradhar bsutra@ndl.gov.in Prof. Saswat Chakrabarti will be added soon
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