Constructions Of Strict Lyapunov Functions
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Constructions Of Strict Lyapunov Functions
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Author : Michael Malisoff
language : en
Publisher: Springer Science & Business Media
Release Date : 2009-06-13
Constructions Of Strict Lyapunov Functions written by Michael Malisoff 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 2009-06-13 with Technology & Engineering categories.
Converse Lyapunov function theory guarantees the existence of strict Lyapunov functions in many situations, but the functions it provides are often abstract and nonexplicit, and therefore may not lend themselves to engineering applications. Often, even when a system is known to be stable, one still needs explicit Lyapunov functions; however, once an appropriate strict Lyapunov function has been constructed, many robustness and stabilization problems can be solved through standard feedback designs or robustness arguments. Non-strict Lyapunov functions are often readily constructed. This book contains a broad repertoire of Lyapunov constructions for nonlinear systems, focusing on methods for transforming non-strict Lyapunov functions into strict ones. Their explicitness and simplicity make them suitable for feedback design, and for quantifying the effects of uncertainty. Readers will benefit from the authors’ mathematical rigor and unifying, design-oriented approach, as well as the numerous worked examples.
Stability And Stabilization Of Nonlinear Systems
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Author : Iasson Karafyllis
language : en
Publisher: Springer Science & Business Media
Release Date : 2011-04-02
Stability And Stabilization Of Nonlinear Systems written by Iasson Karafyllis 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 2011-04-02 with Technology & Engineering categories.
Recently, the subject of nonlinear control systems analysis has grown rapidly and this book provides a simple and self-contained presentation of their stability and feedback stabilization which enables the reader to learn and understand major techniques used in mathematical control theory. In particular: the important techniques of proving global stability properties are presented closely linked with corresponding methods of nonlinear feedback stabilization; a general framework of methods for proving stability is given, thus allowing the study of a wide class of nonlinear systems, including finite-dimensional systems described by ordinary differential equations, discrete-time systems, systems with delays and sampled-data systems; approaches to the proof of classical global stability properties are extended to non-classical global stability properties such as non-uniform-in-time stability and input-to-output stability; and new tools for stability analysis and control design of a wide class of nonlinear systems are introduced. The presentational emphasis of Stability and Stabilization of Nonlinear Systems is theoretical but the theory’s importance for concrete control problems is highlighted with a chapter specifically dedicated to applications and with numerous illustrative examples. Researchers working on nonlinear control theory will find this monograph of interest while graduate students of systems and control can also gain much insight and assistance from the methods and proofs detailed in this book.
Construction Of Global Lyapunov Functions Using Radial Basis Functions
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Author : Peter Giesl
language : en
Publisher: Springer
Release Date : 2007-04-11
Construction Of Global Lyapunov Functions Using Radial Basis Functions written by Peter Giesl and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007-04-11 with Mathematics categories.
The basin of attraction of an equilibrium of an ordinary differential equation can be determined using a Lyapunov function. A new method to construct such a Lyapunov function using radial basis functions is presented in this volume intended for researchers and advanced students from both dynamical systems and radial basis functions. Besides an introduction to both areas and a detailed description of the method, it contains error estimates and many examples.
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.
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.
Safety Factor Profile Control In A Tokamak
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Author : Federico Bribiesca Argomedo
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-11-08
Safety Factor Profile Control In A Tokamak written by Federico Bribiesca Argomedo 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 2013-11-08 with Technology & Engineering categories.
Control of the Safety Factor Profile in a Tokamak uses Lyapunov techniques to address a challenging problem for which even the simplest physically relevant models are represented by nonlinear, time-dependent, partial differential equations (PDEs). This is because of the spatiotemporal dynamics of transport phenomena (magnetic flux, heat, densities, etc.) in the anisotropic plasma medium. Robustness considerations are ubiquitous in the analysis and control design since direct measurements on the magnetic flux are impossible (its estimation relies on virtual sensors) and large uncertainties remain in the coupling between the plasma particles and the radio-frequency waves (distributed inputs). The Brief begins with a presentation of the reference dynamical model and continues by developing a Lyapunov function for the discretized system (in a polytopic linear-parameter-varying formulation). The limitations of this finite-dimensional approach motivate new developments in the infinite-dimensional framework. The text then tackles the construction of an input-to-state-stability Lyapunov function for the infinite-dimensional system that handles the medium anisotropy and provides a common basis for analytical robustness results. This function is used as a control-Lyapunov function and allows the amplitude and nonlinear shape constraints in the control action to be dealt with. Finally, the Brief addresses important application- and implementation-specific concerns. In particular, the coupling of the PDE and the finite-dimensional subsystem representing the evolution of the boundary condition (magnetic coils) and the introduction of profile-reconstruction delays in the control loop (induced by solving a 2-D inverse problem for computing the magnetic flux) is analyzed. Simulation results are presented for various operation scenarios on Tore Supra (simulated with METIS) and on TCV (simulated with RAPTOR). Control of the Safety Factor Profile in a Tokamak will be of interest to both academic and industrially-based researchers interested in nuclear energy and plasma-containment control systems, and graduate students in nuclear and control engineering.
Nonlinear Control Under Nonconstant Delays
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Author : Nikolaos Bekiaris-Liberis
language : en
Publisher: SIAM
Release Date : 2013-09-25
Nonlinear Control Under Nonconstant Delays written by Nikolaos Bekiaris-Liberis and has been published by SIAM this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-09-25 with Mathematics categories.
The authors have developed a methodology for control of nonlinear systems in the presence of long delays, with large and rapid variation in the actuation or sensing path, or in the presence of long delays affecting the internal state of a system. In addition to control synthesis, they introduce tools to quantify the performance and the robustness properties of the designs provided in the book. The book is based on the concept of predictor feedback and infinite-dimensional backstepping transformation for linear systems and the authors guide the reader from the basic ideas of the concept?with constant delays only on the input?all the way through to nonlinear systems with state-dependent delays on the input as well as on system states. Readers will find the book useful because the authors provide elegant and systematic treatments of long-standing problems in delay systems, such as systems with state-dependent delays that arise in many applications. In addition, the authors give all control designs by explicit formulae, making the book especially useful for engineers who have faced delay-related challenges and are concerned with actual implementations and they accompany all control designs with Lyapunov-based analysis for establishing stability and performance guarantees.
Feedback Systems
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Author : Karl Johan Åström
language : en
Publisher: Princeton University Press
Release Date : 2021-02-02
Feedback Systems written by Karl Johan Åström and has been published by Princeton University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-02-02 with Technology & Engineering categories.
The essential introduction to the principles and applications of feedback systems—now fully revised and expanded This textbook covers the mathematics needed to model, analyze, and design feedback systems. Now more user-friendly than ever, this revised and expanded edition of Feedback Systems is a one-volume resource for students and researchers in mathematics and engineering. It has applications across a range of disciplines that utilize feedback in physical, biological, information, and economic systems. Karl Åström and Richard Murray use techniques from physics, computer science, and operations research to introduce control-oriented modeling. They begin with state space tools for analysis and design, including stability of solutions, Lyapunov functions, reachability, state feedback observability, and estimators. The matrix exponential plays a central role in the analysis of linear control systems, allowing a concise development of many of the key concepts for this class of models. Åström and Murray then develop and explain tools in the frequency domain, including transfer functions, Nyquist analysis, PID control, frequency domain design, and robustness. Features a new chapter on design principles and tools, illustrating the types of problems that can be solved using feedback Includes a new chapter on fundamental limits and new material on the Routh-Hurwitz criterion and root locus plots Provides exercises at the end of every chapter Comes with an electronic solutions manual An ideal textbook for undergraduate and graduate students Indispensable for researchers seeking a self-contained resource on control theory
Nonlinear And Adaptive Control With Applications
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Author : Alessandro Astolfi
language : en
Publisher: Springer Science & Business Media
Release Date : 2007-12-06
Nonlinear And Adaptive Control With Applications written by Alessandro Astolfi 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 2007-12-06 with Technology & Engineering categories.
The authors here provide a detailed treatment of the design of robust adaptive controllers for nonlinear systems with uncertainties. They employ a new tool based on the ideas of system immersion and manifold invariance. New algorithms are delivered for the construction of robust asymptotically-stabilizing and adaptive control laws for nonlinear systems. The methods proposed lead to modular schemes that are easier to tune than their counterparts obtained from Lyapunov redesign.
Ordinary Differential Equations With Applications
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Author : Carmen Chicone
language : en
Publisher: Springer Science & Business Media
Release Date : 2006-09-23
Ordinary Differential Equations With Applications written by Carmen Chicone 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 2006-09-23 with Mathematics categories.
Based on a one-year course taught by the author to graduates at the University of Missouri, this book provides a student-friendly account of some of the standard topics encountered in an introductory course of ordinary differential equations. In a second semester, these ideas can be expanded by introducing more advanced concepts and applications. A central theme in the book is the use of Implicit Function Theorem, while the latter sections of the book introduce the basic ideas of perturbation theory as applications of this Theorem. The book also contains material differing from standard treatments, for example, the Fiber Contraction Principle is used to prove the smoothness of functions that are obtained as fixed points of contractions. The ideas introduced in this section can be extended to infinite dimensions.