Overview
- Provides a unique treatment of disturbance attenuation in nonsmooth systems
- Combines the most popular robust control models (H-infinity, backstepping, and sliding mode)
- Contains electromechanical applications with underactuation and complex phenomena
- Rigorous theoretical development supported by experimental results
- Includes supplementary material: sn.pub/extras
Part of the book series: Systems & Control: Foundations & Applications (SCFA)
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Table of contents (11 chapters)
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Front Matter
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Nonsmooth $$\mathcal{H}_{\infty }$$ Control
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Front Matter
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Nonsmooth $$\mathcal{H}_{\infty }$$ Control
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Benchmark Applications
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Front Matter
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Back Matter
Keywords
About this book
This compact monograph is focused on disturbance attenuation in nonsmooth dynamic systems, developing an H∞ approach in the nonsmooth setting. Similar to the standard nonlinear H∞ approach, the proposed nonsmooth design guarantees both the internal asymptotic stability of a nominal closed-loop system and the dissipativity inequality, which states that the size of an error signal is uniformly bounded with respect to the worst-case size of an external disturbance signal. This guarantee is achieved by constructing an energy or storage function that satisfies the dissipativity inequality and is then utilized as a Lyapunov function to ensure the internal stability requirements.
Advanced H∞ Control is unique in the literature for its treatment of disturbance attenuation in nonsmooth systems. It synthesizes various tools, including Hamilton–Jacobi–Isaacs partial differential inequalities as well as Linear Matrix Inequalities. Along with the finite-dimensional treatment, the synthesis is extended to infinite-dimensional setting, involving time-delay and distributed parameter systems. To help illustrate this synthesis, the book focuses on electromechanical applications with nonsmooth phenomena caused by dry friction, backlash, and sampled-data measurements. Special attention is devoted to implementation issues.
Requiring familiarity with nonlinear systems theory, this book will be accessible to g
raduate students interested in systems analysis and design, and is a welcome addition to the literature for researchers and practitioners in these areas.Reviews
“The present book is a research monograph. … it is self-contained, and so the reader who takes the effort to study the book in detail, learns how to design robust controllers for a very general class of systems, such as those described by nonsmooth nonlinear models and those described by partial differential equations.” (Hans Zwart, zbMATH 1328.93005, 2016)
“This monograph addresses the H∞ control problem for a wide class of systems described by ‘finite-/infinite-dimensional, linear/nonlinear, time-invariant/-varying, without/with delay’ equations. … The proposed method allows one to develop powerful algorithms for the H∞ design of nonsmooth systems.” (Hideki Sano, Mathematical Reviews, June, 2015)
Authors and Affiliations
Bibliographic Information
Book Title: Advanced H∞ Control
Book Subtitle: Towards Nonsmooth Theory and Applications
Authors: Yury V. Orlov, Luis T. Aguilar
Series Title: Systems & Control: Foundations & Applications
DOI: https://doi.org/10.1007/978-1-4939-0292-7
Publisher: Birkhäuser New York, NY
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: Springer Science+Business Media New York 2014
Hardcover ISBN: 978-1-4939-0291-0Published: 21 February 2014
Softcover ISBN: 978-1-4939-4442-2Published: 23 August 2016
eBook ISBN: 978-1-4939-0292-7Published: 20 February 2014
Series ISSN: 2324-9749
Series E-ISSN: 2324-9757
Edition Number: 1
Number of Pages: XI, 218
Number of Illustrations: 31 b/w illustrations, 12 illustrations in colour
Topics: Systems Theory, Control, Vibration, Dynamical Systems, Control, Dynamical Systems and Ergodic Theory, Partial Differential Equations, Mathematical and Computational Engineering, Applications of Mathematics