Nonsmooth Lyapunov Analysis In Finite And Infinite Dimensions
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Nonsmooth Lyapunov Analysis In Finite And Infinite Dimensions
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Author : Yury Orlov
language : en
Publisher: Springer Nature
Release Date : 2020-02-08
Nonsmooth Lyapunov Analysis In Finite And Infinite Dimensions written by Yury Orlov and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-02-08 with Technology & Engineering categories.
Nonsmooth Lyapunov Analysis in Finite and Infinite Dimensions provides helpful tools for the treatment of a broad class of dynamical systems that are governed, not only by ordinary differential equations but also by partial and functional differential equations. Existing Lyapunov constructions are extended to discontinuous systems—those with variable structure and impact—by the involvement of nonsmooth Lyapunov functions. The general theoretical presentation is illustrated by control-related applications; the nonsmooth Lyapunov construction is particularly applied to the tuning of sliding-mode controllers in the presence of mismatched disturbances and to orbital stabilization of the bipedal gate. The nonsmooth construction is readily extendible to the control and identification of distributed-parameter and time-delay systems. The first part of the book outlines the relevant fundamentals of benchmark models and mathematical basics. The second concentrates on the construction of nonsmooth Lyapunov functions. Part III covers design and applications material. This book will benefit the academic research and graduate student interested in the mathematics of Lyapunov equations and variable-structure control, stability analysis and robust feedback design for discontinuous systems. It will also serve the practitioner working with applications of such systems. The reader should have some knowledge of dynamical systems theory, but no background in discontinuous systems is required—they are thoroughly introduced in both finite- and infinite-dimensional settings.
Discontinuous Systems
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Author : Yury V. Orlov
language : en
Publisher: Springer Science & Business Media
Release Date : 2008-10-28
Discontinuous Systems written by Yury V. Orlov and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008-10-28 with Technology & Engineering categories.
Discontinuous Systems develops nonsmooth stability analysis and discontinuous control synthesis based on novel modeling of discontinuous dynamic systems, operating under uncertain conditions. While being primarily a research monograph devoted to the theory of discontinuous dynamic systems, no background in discontinuous systems is required; such systems are introduced in the book at the appropriate conceptual level. Being developed for discontinuous systems, the theory is successfully applied to their subclasses – variable-structure and impulsive systems – as well as to finite- and infinite-dimensional systems such as distributed-parameter and time-delay systems. The presentation concentrates on algorithms rather than on technical implementation although theoretical results are illustrated by electromechanical applications. These specific applications complete the book and, together with the introductory theoretical constituents bring some elements of the tutorial to the text.
Advanced H Control
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Author : Yury V. Orlov
language : en
Publisher: Springer Science & Business Media
Release Date : 2014-02-20
Advanced H Control written by Yury V. Orlov and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-02-20 with Science categories.
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.
Set Valued Convex And Nonsmooth Analysis In Dynamics And Control
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Author : Rafal K. Goebel
language : en
Publisher: SIAM
Release Date : 2024-06-26
Set Valued Convex And Nonsmooth Analysis In Dynamics And Control written by Rafal K. Goebel and has been published by SIAM this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-06-26 with Mathematics categories.
Set-valued analysis, convex analysis, and nonsmooth analysis are relatively modern branches of mathematical analysis that have become increasingly relevant in current control theory and control engineering literature. This book serves as a broad introduction to analytical tools in these fields and to their applications in dynamical and control systems and is the first to cover these topics with this scope and at this level. Both continuous-time and discrete-time mutlivalued dynamics, modeled by differential and difference inclusions, are considered. Set-Valued, Convex, and Nonsmooth Analysis in Dynamics and Control: An Introduction is aimed at graduate students in control engineering and applied mathematics and researchers in control engineering who have no prior exposure to set-valued, convex, and nonsmooth analysis. The book will also be of interest to advanced undergraduate mathematics students and mathematicians with no prior exposure to the topic. The expected mathematical background is a course on nonlinear differential equations / dynamical systems and a course on real analysis. Knowledge of some control theory is helpful, but not essential.
In Stability Of Differential Inclusions
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Author : Philipp Braun
language : en
Publisher: Springer Nature
Release Date : 2021-07-12
In Stability Of Differential Inclusions written by Philipp Braun and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-07-12 with Mathematics categories.
Lyapunov methods have been and are still one of the main tools to analyze the stability properties of dynamical systems. In this monograph, Lyapunov results characterizing the stability and stability of the origin of differential inclusions are reviewed. To characterize instability and destabilizability, Lyapunov-like functions, called Chetaev and control Chetaev functions in the monograph, are introduced. Based on their definition and by mirroring existing results on stability, analogue results for instability are derived. Moreover, by looking at the dynamics of a differential inclusion in backward time, similarities and differences between stability of the origin in forward time and instability in backward time, and vice versa, are discussed. Similarly, the invariance of the stability and instability properties of the equilibria of differential equations with respect to scaling are summarized. As a final result, ideas combining control Lyapunov and control Chetaev functions to simultaneously guarantee stability, i.e., convergence, and instability, i.e., avoidance, are outlined. The work is addressed at researchers working in control as well as graduate students in control engineering and applied mathematics.
Generalized Homogeneity In Systems And Control
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Author : Andrey Polyakov
language : en
Publisher: Springer Nature
Release Date : 2020-02-05
Generalized Homogeneity In Systems And Control written by Andrey Polyakov and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-02-05 with Technology & Engineering categories.
This monograph introduces the theory of generalized homogeneous systems governed by differential equations in both Euclidean (finite-dimensional) and Banach/Hilbert (infinite-dimensional) spaces. It develops methods of stability and robustness analysis, control design, state estimation and discretization of homogeneous control systems. Generalized Homogeneity in Systems and Control is structured in two parts. Part I discusses various models of control systems and related tools for their analysis, including Lyapunov functions. Part II deals with the analysis and design of homogeneous control systems. Some of the key features of the text include: mathematical models of dynamical systems in finite-dimensional and infinite-dimensional spaces; the theory of linear dilations in Banach spaces; homogeneous control and estimation; simple methods for an "upgrade" of existing linear control laws; numerical schemes for a consistent digital implementation of homogeneous algorithms; and experiments confirming an improvement of PID controllers. The advanced mathematical material will be of interest to researchers, mathematicians working in control theory and mathematically oriented control engineers.
New Horizons For Fuzzy Logic Neural Networks And Metaheuristics
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Author : Oscar Castillo
language : en
Publisher: Springer Nature
Release Date :
New Horizons For Fuzzy Logic Neural Networks And Metaheuristics written by Oscar Castillo and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on with categories.
Dissipative Systems Analysis And Control
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Author : Bernard Brogliato
language : en
Publisher: Springer
Release Date : 2019-07-03
Dissipative Systems Analysis And Control written by Bernard Brogliato and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-07-03 with Technology & Engineering categories.
This second edition of Dissipative Systems Analysis and Control has been substantially reorganized to accommodate new material and enhance its pedagogical features. It examines linear and nonlinear systems with examples of both in each chapter. Also included are some infinite-dimensional and nonsmooth examples. Throughout, emphasis is placed on the use of the dissipative properties of a system for the design of stable feedback control laws.
Stability Of Infinite Dimensional Stochastic Differential Equations With Applications
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Author : Kai Liu
language : en
Publisher: CRC Press
Release Date : 2005-08-23
Stability Of Infinite Dimensional Stochastic Differential Equations With Applications written by Kai Liu and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2005-08-23 with Mathematics categories.
Stochastic differential equations in infinite dimensional spaces are motivated by the theory and analysis of stochastic processes and by applications such as stochastic control, population biology, and turbulence, where the analysis and control of such systems involves investigating their stability. While the theory of such equations is well establ
Nonsmooth Optimization And Related Topics
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Author : F.H. Clarke
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-11-11
Nonsmooth Optimization And Related Topics written by F.H. Clarke and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-11-11 with Science categories.
This volume contains the edited texts of the lect. nres presented at the International School of Mathematics devoted to Nonsmonth Optimization, held from . June 20 to July I, 1988. The site for the meeting was the "Ettore ~Iajorana" Centre for Sci entific Culture in Erice, Sicily. In the tradition of these meetings the main purpose was to give the state-of-the-art of an important and growing field of mathematics, and to stimulate interactions between finite-dimensional and infinite-dimensional op timization. The School was attended by approximately 80 people from 23 countries; in particular it was possible to have some distinguished lecturers from the SO\·iet Union, whose research institutions are here gratt-fnlly acknowledged. Besides the lectures, several seminars were delivered; a special s·~ssion was devoted to numerical computing aspects. The result was a broad exposure. gi ·. ring a deep knowledge of the present research tendencies in the field. We wish to express our appreciation to all the participants. Special mention 5hould be made of the Ettorc ;. . Iajorana Centre in Erice, which helped provide a stimulating and rewarding experience, and of its staff which was fundamental for the success of the meeting. j\, loreover, WP want to extend uur deep appreci