### Model-Free
Stabilization by Extremum Seeking

Alexander Scheinker
and Miroslav Krstic

Springer, 2017

127
pages, hardcover

ISBN 978-3-319-50790-3

Preface
and Contents

Contents:

Preface

1. Introduction

2. Weak Limit Averaging for Studying the
Dynamics of Extremum Seeking-Stabilized Systems

3. Minimization of Lyapunov
Functions

4. Control Affine Systems

5. Non-C^{2} ES

6. Bounded ES

7. Extremum Seeking
for Stabilization of Systems Not Affine in Control

8. General Choice of ES Dithers

9. Application Study: Particle Accelerator
Tuning

10. Conclusions

References

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Publisher's description:

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.