Model-Free Stabilization by Extremum Seeking

✍ Scribed by Alexander Scheinker, Miroslav Krstić (auth.)

• Publisher: Springer International Publishing
• Year: 2017
• Tongue: English
• Leaves: 129
• Series: SpringerBriefs in Electrical and Computer Engineering
• Edition: 1
• Category: Library

✦ Synopsis

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.

✦ Table of Contents

Front Matter....Pages i-ix
Introduction....Pages 1-11
Weak Limit Averaging for Studying the Dynamics of Extremum Seeking-Stabilized Systems....Pages 13-23
Minimization of Lyapunov Functions....Pages 25-29
Control Affine Systems....Pages 31-54
Non-C (^{2}) ES....Pages 55-63
Bounded ES....Pages 65-74
Extremum Seeking for Stabilization of Systems Not Affine in Control....Pages 75-89
General Choice of ES Dithers....Pages 91-99
Application Study: Particle Accelerator Tuning....Pages 101-115
Conclusions....Pages 117-117
Back Matter....Pages 119-127

✦ Subjects

Control;Systems Theory, Control;Calculus of Variations and Optimal Control; Optimization;Particle Acceleration and Detection, Beam Physics;Artificial Intelligence (incl. Robotics)