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Model-Free Stabilization by Extremum Seeking

Part of the SpringerBriefs in Electrical and Computer Engineering Book Series

DOI: 10.1007/978-3-319-50790-3

ISBN: 978-3-319-50789-7

Publisher: Springer International Publishing - Springer Journals

Dec 25, 2016

1 - 10 of 10 Chapters

Available

Introduction

Scheinker, Alexander; Krstić, Miroslav

Pages: 1 –11

[In this chapter we introduce extremum seeking (ES) as a method for stabilization of unknown, nonlinear, time-varying systems, by utilizing an ES approach directly as the feedback controller itself. Our “extremum seeking for stabilization” (ESS) consists of employing the control Lyapunov function...
Available

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

Scheinker, Alexander; Krstić, Miroslav

Pages: 13 –23

[In this chapter we review some functional analysis and prove the main weak limit averaging theorem, Theorem 2.3, upon which the main results of this book are based. We also work out a simple example in detail to show exactly how Theorem 2.3 is applied.]
Available

Minimization of Lyapunov Functions

Scheinker, Alexander; Krstić, Miroslav

Pages: 25 –29

[In this chapter we give a general overview of utilizing extremum seeking (ES) to stabilize a large class of systems, and discuss the strength of the approach for systems with unknown control directions, providing a stabilizing controller that is more robust than traditional Nussbaum type control.]
Available

Control Affine Systems

Scheinker, Alexander; Krstić, Miroslav

Pages: 31 –54

[In this chapter we utilize extremum seeking (ES) to stabilize a large class of systems affine in control, including time-varying nonlinear systems. We work out the details of stability proofs and provide several numerical examples of applying ES for stabilization.]
Available

Non-C\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$^{2}$$\end{document} ES

Scheinker, Alexander; Krstić, Miroslav

Pages: 55 –63

[This chapter introduces a form of extremum seeking (ES) whose control effort settles to zero as the system’s trajectory approaches equilibrium.]
Available

Bounded ES

Scheinker, Alexander; Krstić, Miroslav

Pages: 65 –74

[In this chapter we present a form of extremum seeking (ES) in which the unknown function being minimized enters the system?s dynamics as the argument of a cosine or sine term, thereby guaranteeing known bounds on update rates and control efforts. We present general n-dimensional optimization and...
Available

Extremum Seeking for Stabilization of Systems Not Affine in Control

Scheinker, Alexander; Krstić, Miroslav

Pages: 75 –89

[Although most extremum seeking for stabilization results have been presented for systems affine in control, in most physical systems the control effort enters the system’s dynamics through a nonlinear function, such as an input with deadzone and saturation. In this chapter, we develop...
Available

General Choice of ES Dithers

Scheinker, Alexander; Krstić, Miroslav

Pages: 91 –99

[In this chapter we establish a simple and general extension of the previously developed bounded form of ES to a general class of oscillatory functions, including functions discontinuous with respect to time, such as triangle or square waves with dead time. We establish our main results by...
Available

Application Study: Particle Accelerator Tuning

Scheinker, Alexander; Krstić, Miroslav

Pages: 101 –115

[In this chapter we present a simulation study of applying the ES method for optimization of a particle accelerator with time-varying beam and component characteristics and we also describe the experimental results of applying ES in hardware for resonance control. We demonstrate the main...
Available

Conclusions

Scheinker, Alexander; Krstić, Miroslav

Pages: 117 –117

[This book presents a new application of Extremum Seeking, as a method for stabilization of unknown systems as well as trajectory tracking and optimization. The stabilization of unknown systems is possible due to the controller’s ability to perform a gradient descent of unknown functions or of...

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