Model-Free Stabilization by Extremum Seeking

  • Alexander Scheinker
  • Miroslav Krstić

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-ix
  2. Alexander Scheinker, Miroslav Krstić
    Pages 1-11
  3. Alexander Scheinker, Miroslav Krstić
    Pages 25-29
  4. Alexander Scheinker, Miroslav Krstić
    Pages 31-54
  5. Alexander Scheinker, Miroslav Krstić
    Pages 55-63
  6. Alexander Scheinker, Miroslav Krstić
    Pages 65-74
  7. Alexander Scheinker, Miroslav Krstić
    Pages 75-89
  8. Alexander Scheinker, Miroslav Krstić
    Pages 91-99
  9. Alexander Scheinker, Miroslav Krstić
    Pages 101-115
  10. Alexander Scheinker, Miroslav Krstić
    Pages 117-117
  11. Back Matter
    Pages 119-127

About this book

Introduction

With this brief, the authors present algorithms for model-free stabilization of unstable dynamic systems. An extremum-seeking algorithm assigns the role of a cost function to the dynamic system’s control Lyapunov function (clf) aiming at its minimization. The minimization of the clf drives the clf to zero and achieves asymptotic stabilization. This approach does not rely on, or require knowledge of, the system model. Instead, it employs periodic perturbation signals, along with the clf. The same effect is achieved as by using clf-based feedback laws that profit from modeling knowledge, but in a time-average sense. Rather than use integrals of the systems vector field, we employ Lie-bracket-based (i.e., derivative-based) averaging.

The brief contains numerous examples and applications, including examples with unknown control directions and experiments with charged particle accelerators. It is intended for theoretical control engineers and mathematicians, and practitioners working in various industrial areas and in robotics.

Keywords

Stabilization of Unknown Systems Nonlinear Systems Uncertain Systems Extremum Seeking Particle Accelerator Tuning Uncertain Systems

Authors and affiliations

  • Alexander Scheinker
    • 1
  • Miroslav Krstić
    • 2
  1. 1.Low-Level RF Control GroupLos Alamos National LaboratoryLos AlamosUSA
  2. 2.Department of Mechanical and Aerospace EngineeringUniversity of California, San DiegoLa JollaUSA

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-319-50790-3
  • Copyright Information The Author(s) 2017
  • Publisher Name Springer, Cham
  • eBook Packages Engineering
  • Print ISBN 978-3-319-50789-7
  • Online ISBN 978-3-319-50790-3
  • Series Print ISSN 2191-8112
  • Series Online ISSN 2191-8120
  • About this book