Authors:
- For engineers the text develops a stochastic version of increasingly popular deterministic extremum-seeking algorithms
- Demonstrates to the mathematician how stochastic averaging theory can be used as a tool for studying stability rather than just approximation
- Stochastic algorithms are intuitive and connect with the huge field of stochastic optimization
- Shows how control ideas derived from study of a biological system can be generalized into other widely-different fields of application
- Includes supplementary material: sn.pub/extras
Part of the book series: Communications and Control Engineering (CCE)
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Table of contents (11 chapters)
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Front Matter
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Back Matter
About this book
Stochastic averaging theorems are developed for the analysis of continuous-time nonlinear systems with random forcing, removing prior restrictions on nonlinearity growth and on the finiteness of the time interval. The new stochastic averaging theorems are usable not only as approximation tools but also for providing stability guarantees.
Stochastic extremum-seeking algorithms are introduced for optimization of systems without available models. Both gradient- and Newton-based algorithms are presented, offering the user the choice between the simplicity of implementation (gradient) and the ability to achieve a known, arbitrary convergence rate (Newton).
The design of algorithms for non-cooperative/adversarial games is described. The analysis of their convergence to Nash equilibria is provided. The algorithms are illustrated on models of economic competition and on problems of the deployment of teams of robotic vehicles.
Bacterial locomotion, such as chemotaxis in E. coli, is explored with the aim of identifying two simple feedback laws for climbing nutrient gradients. Stochastic extremum seeking is shown to be a biologically-plausible interpretation for chemotaxis. For the same chemotaxis-inspired stochastic feedback laws, the book also provides a detailed analysis of convergence for models of nonholonomic robotic vehicles operating in GPS-denied environments.
The book contains block diagrams and several simulation examples, including examples arising from bacterial locomotion, multi-agent robotic systems, and economic market models.
Stochastic Averaging and Extremum Seeking will be informative for control engineers from backgrounds in electrical, mechanical, chemical and aerospace engineering and to applied mathematicians. Economics researchers, biologists, biophysicists and roboticists will find the applications examples instructive.
Reviews
From the book reviews:
“This research monograph presents and consolidates new results on the well-known topic of stochastic averaging and in the emerging area of stochastic extremum seeking. … The monograph develops averaging from scratch for ordinary differential equations in deterministic and stochastic settings. … This book will be of interest to researchers interested in stochastic search techniques applied to a large variety of engineering systems.” (IEEE Control Systems Magazine, October, 2013)Authors and Affiliations
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Department of Mathematics, Southeast University, Nanjing, China, People's Republic
Shu-Jun Liu
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Dept. Mechanical & Aerospace Engin., University of California, San Diego, La Jolla, USA
Miroslav Krstic
About the authors
Shujun Liu is a young researcher in mathematics and control theory in China with strong connections with the leading research groups in control theory at the Chinese Academy of Sciences. Her doctoral work on stochastic stability and stabilization has had considerable influence on a number of research groups in China who have taken on this topic after her initial work with her doctoral advisor Professor Jifeng Zhang.
Much of the material of this book was developed while the first author was a postdoctoral scholar with the second author at University of California, San Diego.
Bibliographic Information
Book Title: Stochastic Averaging and Stochastic Extremum Seeking
Authors: Shu-Jun Liu, Miroslav Krstic
Series Title: Communications and Control Engineering
DOI: https://doi.org/10.1007/978-1-4471-4087-0
Publisher: Springer London
eBook Packages: Engineering, Engineering (R0)
Copyright Information: Springer-Verlag London 2012
Hardcover ISBN: 978-1-4471-4086-3Published: 17 June 2012
Softcover ISBN: 978-1-4471-6185-1Published: 17 July 2014
eBook ISBN: 978-1-4471-4087-0Published: 16 June 2012
Series ISSN: 0178-5354
Series E-ISSN: 2197-7119
Edition Number: 1
Number of Pages: XII, 224
Topics: Control and Systems Theory, Calculus of Variations and Optimal Control; Optimization, Economic Theory/Quantitative Economics/Mathematical Methods, Systems Biology, Robotics and Automation, Systems Theory, Control