Advances in Numerical Mathematics

Fast Numerical Methods for Mixed-Integer Nonlinear Model-Predictive Control

Authors: Kirches, Christian

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About this book

Current industrial practice knows many optimization tasks that can be cast as mixed-integer optimal control problems. Due to the combinatorial character of these problems, the computation of optimal solutions under real-time constraints is still a demanding challenge.

Starting with Bock's direct multiple shooting method for optimal control, Christian Kirches develops a fast numerical algorithm of wide applicability that efficiently solves mixed-integer nonlinear optimal control problems. He uses convexification and relaxation techniques to obtain computationally tractable reformulations for which feasibility and optimality certificates can be given even after discretization and rounding. In a sequential quadratic programming framework, extensive exploitation of arising structures in an active set method ultimately brings the developed algorithm towards real-time feasibility.

About the authors

Dr. Christian Kirches is a postdoctoral researcher in the simulation and optimization group at the chair of Professor Dr. Dr. h.c. Hans Georg Bock at the Interdisciplinary Center for Scientific Computing (IWR) of Heidelberg University.

Reviews

From the book reviews:

“The book under review gives a useful introduction and presents valuable new contributions in this topic. … The material is very clearly written and certain parts … may well support graduate education. The targeted audience of the book is applied mathematicians and engineers.” (Gábor Szederkényi, Mathematical Reviews, January, 2015)


Table of contents (10 chapters)

  • Introduction

    Kirches, Christian

    Pages 1-12

  • The Direct Multiple Shooting Method for Optimal Control

    Kirches, Christian

    Pages 13-29

  • Mixed–Integer Optimal Control

    Kirches, Christian

    Pages 31-60

  • Constrained Nonlinear Programming

    Kirches, Christian

    Pages 61-87

  • Mixed–Integer Real–Time Iterations

    Kirches, Christian

    Pages 89-116

Buy this book

eBook $109.00
price for USA (gross)
  • ISBN 978-3-8348-8202-8
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Softcover $139.00
price for USA
  • ISBN 978-3-8348-1572-9
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
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Bibliographic Information

Bibliographic Information
Book Title
Fast Numerical Methods for Mixed-Integer Nonlinear Model-Predictive Control
Authors
Series Title
Advances in Numerical Mathematics
Copyright
2011
Publisher
Vieweg+Teubner Verlag
Copyright Holder
Vieweg+Teubner Verlag | Springer Fachmedien Wiesbaden GmbH, Wiesbaden
eBook ISBN
978-3-8348-8202-8
DOI
10.1007/978-3-8348-8202-8
Softcover ISBN
978-3-8348-1572-9
Series ISSN
1616-2994
Edition Number
1
Number of Pages
XX, 367
Number of Illustrations and Tables
64 b/w illustrations
Topics