SpringerBriefs in Electrical and Computer Engineering: Mathematical Foundations and Applications

Prodan, Ionela; Stoican, Florin; Olaru, Sorin; Niculescu, Silviu-Iulian

In this book, the authors propose efficient characterizations of the non-convex regions that appear in many control problems, such as those involving collision/obstacle avoidance and, in a broader sense, in the description of feasible sets for optimization-based control design involving contradictory objectives. 

The text deals with a large class of systems that require the solution of appropriate optimization problems over a feasible region, which is neither convex nor compact. The proposed approach uses the combinatorial notion of hyperplane arrangement, partitioning the space by a finite collection of hyperplanes, to describe non-convex regions efficiently. Mixed-integer programming techniques are then applied to propose acceptable formulations of the overall problem. Multiple constructions may arise from the same initial problem, and their complexity under various parameters - space dimension, number of binary variables, etc. - is also discussed.

This book is auseful tool for academic researchers and graduate students interested in non-convex systems working in control engineering area, mobile robotics and/or optimal planning and decision-making.

Details

Published by: Springer

Publication Date: 2015-12-02

Format: Paperback

ISBN-13: 9783319269931

DOI: 10.1007/978-3-319-26995-5

Dimensions: 235cm x155cm

Pages: 107