About this book
Stochastic Averaging and Stochastic Extremum Seeking develops methods of mathematical analysis inspired by the interest in reverse engineering and analysis of bacterial convergence by chemotaxis and to apply similar stochastic optimization techniques in other environments.
The first half of the text presents significant advances in stochastic averaging theory, necessitated by the fact that existing theorems are restricted to systems with linear growth, globally exponentially stable average models, vanishing stochastic perturbations, and prevent analysis over infinite time horizon.
The second half of the text introduces stochastic extremum seeking algorithms for model-free optimization of systems in real time using stochastic perturbations for estimation of their gradients. 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.
The Communications and Control Engineering series reports major technological advances which have potential for great impact in the fields of communication and control. It reflects research in industrial and academic institutions around the world so that the readership can exploit new possibilities as they become available.
- Book Title Stochastic Averaging and Stochastic Extremum Seeking
- Series Title Communications and Control Engineering
- DOI https://doi.org/10.1007/978-1-4471-4087-0
- Copyright Information Springer-Verlag London 2012
- Publisher Name Springer, London
- eBook Packages Engineering Engineering (R0)
- Hardcover ISBN 978-1-4471-4086-3
- Softcover ISBN 978-1-4471-6185-1
- eBook ISBN 978-1-4471-4087-0
- Series ISSN 0178-5354
- Edition Number 1
- Number of Pages XII, 224
- Number of Illustrations 0 b/w illustrations, 0 illustrations in colour
Control and Systems Theory
Calculus of Variations and Optimal Control; Optimization
Economic Theory/Quantitative Economics/Mathematical Methods
Robotics and Automation
Systems Theory, Control
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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)