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Mixed-Integer Representations in Control Design

Mathematical Foundations and Applications

  • Ionela Prodan
  • Florin Stoican
  • Sorin Olaru
  • Silviu-Iulian Niculescu

Part of the SpringerBriefs in Electrical and Computer Engineering book series (BRIEFSELECTRIC)

Also part of the SpringerBriefs in Control, Automation and Robotics book sub series (BRIEFSCONTROL)

Table of contents

  1. Front Matter
    Pages i-xii
  2. Ionela Prodan, Florin Stoican, Sorin Olaru, Silviu-Iulian Niculescu
    Pages 1-9
  3. Ionela Prodan, Florin Stoican, Sorin Olaru, Silviu-Iulian Niculescu
    Pages 11-34
  4. Ionela Prodan, Florin Stoican, Sorin Olaru, Silviu-Iulian Niculescu
    Pages 35-56
  5. Ionela Prodan, Florin Stoican, Sorin Olaru, Silviu-Iulian Niculescu
    Pages 57-89
  6. Ionela Prodan, Florin Stoican, Sorin Olaru, Silviu-Iulian Niculescu
    Pages 91-93
  7. Back Matter
    Pages 95-107

About this book

Introduction

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 a useful 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.

Keywords

Hyperplane Arrangements Mixed-integer Programming Non-convex Constraints Optimization-based Control Design Set Theory

Authors and affiliations

  • Ionela Prodan
    • 1
  • Florin Stoican
    • 2
  • Sorin Olaru
    • 3
  • Silviu-Iulian Niculescu
    • 4
  1. 1.Laboratory of Conception and Integration of SystemsUniversité Grenoble AlpesValenceFrance
  2. 2.Department of Automatic Control and Systems EngineeringPolitehnica University of BucharestBucharestRomania
  3. 3.Laboratory of Signals and SystemsCentraleSupélec - CNRS - Université Paris-Sud, Université Paris-SaclayGif-sur-YvetteFrance
  4. 4.Laboratory of Signals and Systems (L2S, UMR CNRS 8506)CNRS - CentraleSupélec - Université Paris-Sud, Université Paris-SaclayGif-sur-YvetteFrance

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-319-26995-5
  • Copyright Information The Author(s) 2016
  • Publisher Name Springer, Cham
  • eBook Packages Engineering
  • Print ISBN 978-3-319-26993-1
  • Online ISBN 978-3-319-26995-5
  • Series Print ISSN 2191-8112
  • Series Online ISSN 2191-8120
  • Buy this book on publisher's site
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