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

  • Book
  • © 2011

Overview

Authors:
  1. Christian Kirches
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Part of the book series: Advances in Numerical Mathematics (ANUM)

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Table of contents (10 chapters)

  1. Front Matter

    Pages i-xx
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  2. Introduction

    • Christian Kirches
    Pages 1-12

  3. The Direct Multiple Shooting Method for Optimal Control

    • Christian Kirches
    Pages 13-29

  4. Mixed–Integer Optimal Control

    • Christian Kirches
    Pages 31-60

  5. Constrained Nonlinear Programming

    • Christian Kirches
    Pages 61-87

  6. Mixed–Integer Real–Time Iterations

    • Christian Kirches
    Pages 89-116

  7. Outer Convexification of Constraints

    • Christian Kirches
    Pages 117-139

  8. A Nonconvex Parametric SQP Method

    • Christian Kirches
    Pages 141-173

  9. Linear Algebra for Block Structured QPs

    • Christian Kirches
    Pages 175-204

  10. Matrix Updates for the Block Structured Factorization

    • Christian Kirches
    Pages 205-236

  11. Numerical Results

    • Christian Kirches
    Pages 237-319

  12. Back Matter

    Pages 321-367
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Keywords

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.

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)

About the author

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.

Bibliographic Information

  • Book Title: Fast Numerical Methods for Mixed-Integer Nonlinear Model-Predictive Control

  • Authors: Christian Kirches

  • Series Title: Advances in Numerical Mathematics

  • DOI: https://doi.org/10.1007/978-3-8348-8202-8

  • Publisher: Vieweg+Teubner Verlag Wiesbaden

  • eBook Packages: Computer Science, Computer Science (R0)

  • Copyright Information: Vieweg+Teubner Verlag | Springer Fachmedien Wiesbaden GmbH, Wiesbaden 2011

  • Softcover ISBN: 978-3-8348-1572-9Published: 15 September 2011

  • eBook ISBN: 978-3-8348-8202-8Published: 23 November 2011

  • Series ISSN: 1616-2994

  • Edition Number: 1

  • Number of Pages: XX, 367

  • Number of Illustrations: 64 b/w illustrations

  • Topics: Simulation and Modeling, Mathematics, general

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