Input To State Stability For Pdes

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Input To State Stability For Pdes

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Author : Iasson Karafyllis
language : en
Publisher: Springer
Release Date : 2018-06-07

Input To State Stability For Pdes written by Iasson Karafyllis and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-06-07 with Technology & Engineering categories.

This book lays the foundation for the study of input-to-state stability (ISS) of partial differential equations (PDEs) predominantly of two classes—parabolic and hyperbolic. This foundation consists of new PDE-specific tools. In addition to developing ISS theorems, equipped with gain estimates with respect to external disturbances, the authors develop small-gain stability theorems for systems involving PDEs. A variety of system combinations are considered: PDEs (of either class) with static maps; PDEs (again, of either class) with ODEs; PDEs of the same class (parabolic with parabolic and hyperbolic with hyperbolic); and feedback loops of PDEs of different classes (parabolic with hyperbolic). In addition to stability results (including ISS), the text develops existence and uniqueness theory for all systems that are considered. Many of these results answer for the first time the existence and uniqueness problems for many problems that have dominated the PDE control literature of the last two decades, including—for PDEs that include non-local terms—backstepping control designs which result in non-local boundary conditions. Input-to-State Stability for PDEs will interest applied mathematicians and control specialists researching PDEs either as graduate students or full-time academics. It also contains a large number of applications that are at the core of many scientific disciplines and so will be of importance for researchers in physics, engineering, biology, social systems and others.

Extremum Seeking Through Delays And Pdes

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Author : Tiago Roux Oliveira
language : en
Publisher: SIAM
Release Date : 2022-12-05

Extremum Seeking Through Delays And Pdes written by Tiago Roux Oliveira and has been published by SIAM this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-12-05 with Mathematics categories.

Extremum Seeking through Delays and PDEs, the first book on the topic, expands the scope of applicability of the extremum seeking method, from static and finite-dimensional systems to infinite-dimensional systems. Readers will find numerous algorithms for model-free real-time optimization are developed and their convergence guaranteed, extensions from single-player optimization to noncooperative games, under delays and PDEs, are provided, the delays and PDEs are compensated in the control designs using the PDE backstepping approach, and stability is ensured using infinite-dimensional versions of averaging theory, and accessible and powerful tools for analysis. This book is intended for control engineers in all disciplines (electrical, mechanical, aerospace, chemical), mathematicians, physicists, biologists, and economists. It is appropriate for graduate students, researchers, and industrial users.

Delay Compensation For Nonlinear Adaptive And Pde Systems

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Author : Miroslav Krstic
language : en
Publisher: Birkhäuser
Release Date : 2010-04-29

Delay Compensation For Nonlinear Adaptive And Pde Systems written by Miroslav Krstic and has been published by Birkhäuser this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010-04-29 with Mathematics categories.

Shedding light on new opportunities in predictor feedback, this book significantly broadens the set of techniques available to a mathematician or engineer working on delay systems. It is a collection of tools and techniques that make predictor feedback ideas applicable to nonlinear systems, systems modeled by PDEs, systems with highly uncertain or completely unknown input/output delays, and systems whose actuator or sensor dynamics are modeled by more general hyperbolic or parabolic PDEs, rather than by pure delay. Replete with examples, Delay Compensation for Nonlinear, Adaptive, and PDE Systems is an excellent reference guide for graduate students, researchers, and professionals in mathematics, systems control, as well as chemical, mechanical, electrical, computer, aerospace, and civil/structural engineering. Parts of the book may be used in graduate courses on general distributed parameter systems, linear delay systems, PDEs, nonlinear control, state estimator and observers, adaptive control, robust control, or linear time-varying systems.

Boundary Control Of Pdes

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Author : Miroslav Krstic
language : en
Publisher: SIAM
Release Date : 2008-01-01

Boundary Control Of Pdes written by Miroslav Krstic and has been published by SIAM this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008-01-01 with Mathematics categories.

The text's broad coverage includes parabolic PDEs; hyperbolic PDEs of first and second order; fluid, thermal, and structural systems; delay systems; PDEs with third and fourth derivatives in space (including variants of linearized Ginzburg-Landau, Schrodinger, Kuramoto-Sivashinsky, KdV, beam, and Navier-Stokes equations); real-valued as well as complex-valued PDEs; stabilization as well as motion planning and trajectory tracking for PDEs; and elements of adaptive control for PDEs and control of nonlinear PDEs.

Robust Nonlinear Control Design

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Author : Randy A. Freeman
language : en
Publisher: Springer Science & Business Media
Release Date : 2009-05-21

Robust Nonlinear Control Design written by Randy A. Freeman 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 2009-05-21 with Science categories.

The purpose of the book is to summarize Lyapunov design techniques for nonlinear systems and to raise important issues concerning large-signal robustness and performance. The authors have been the first to address some of these issues, and they report their findings in this text. For example, they identify two potential sources of excessive control effort in Lyapunov design techniques and show how such effort can be greatly reduced. The researcher who wishes to enter the field of robust nonlinear control could use this book as a source of new research topics. For those already active in the field, the book may serve as a reference to a recent body of significant work. Finally, the design engineer faced with a nonlinear control problem will benefit from the techniques presented here.

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.

Petsc For Partial Differential Equations Numerical Solutions In C And Python

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Author : Ed Bueler
language : en
Publisher: SIAM
Release Date : 2020-10-22

Petsc For Partial Differential Equations Numerical Solutions In C And Python written by Ed Bueler and has been published by SIAM this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-10-22 with Mathematics categories.

The Portable, Extensible Toolkit for Scientific Computation (PETSc) is an open-source library of advanced data structures and methods for solving linear and nonlinear equations and for managing discretizations. This book uses these modern numerical tools to demonstrate how to solve nonlinear partial differential equations (PDEs) in parallel. It starts from key mathematical concepts, such as Krylov space methods, preconditioning, multigrid, and Newton’s method. In PETSc these components are composed at run time into fast solvers. Discretizations are introduced from the beginning, with an emphasis on finite difference and finite element methodologies. The example C programs of the first 12 chapters, listed on the inside front cover, solve (mostly) elliptic and parabolic PDE problems. Discretization leads to large, sparse, and generally nonlinear systems of algebraic equations. For such problems, mathematical solver concepts are explained and illustrated through the examples, with sufficient context to speed further development. PETSc for Partial Differential Equations addresses both discretizations and fast solvers for PDEs, emphasizing practice more than theory. Well-structured examples lead to run-time choices that result in high solver performance and parallel scalability. The last two chapters build on the reader’s understanding of fast solver concepts when applying the Firedrake Python finite element solver library. This textbook, the first to cover PETSc programming for nonlinear PDEs, provides an on-ramp for graduate students and researchers to a major area of high-performance computing for science and engineering. It is suitable as a supplement for courses in scientific computing or numerical methods for differential equations.

Finite Difference Methods For Ordinary And Partial Differential Equations

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Author : Randall J. LeVeque
language : en
Publisher: SIAM
Release Date : 2007-01-01

Finite Difference Methods For Ordinary And Partial Differential Equations written by Randall J. LeVeque and has been published by SIAM this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007-01-01 with Mathematics categories.

This book introduces finite difference methods for both ordinary differential equations (ODEs) and partial differential equations (PDEs) and discusses the similarities and differences between algorithm design and stability analysis for different types of equations. A unified view of stability theory for ODEs and PDEs is presented, and the interplay between ODE and PDE analysis is stressed. The text emphasizes standard classical methods, but several newer approaches also are introduced and are described in the context of simple motivating examples.

Well Posed Linear Systems

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Author : Olof J. Staffans
language : en
Publisher: Cambridge University Press
Release Date : 2005-02-24

Well Posed Linear Systems written by Olof J. Staffans and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2005-02-24 with Mathematics categories.

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Delay Compensation For Nonlinear Adaptive And Pde Systems

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Author : Miroslav Krstic
language : en
Publisher: Springer Science & Business Media
Release Date : 2010-01-23

Delay Compensation For Nonlinear Adaptive And Pde Systems written by Miroslav Krstic 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 2010-01-23 with Mathematics categories.

Shedding light on new opportunities in predictor feedback, this book significantly broadens the set of techniques available to a mathematician or engineer working on delay systems. It is a collection of tools and techniques that make predictor feedback ideas applicable to nonlinear systems, systems modeled by PDEs, systems with highly uncertain or completely unknown input/output delays, and systems whose actuator or sensor dynamics are modeled by more general hyperbolic or parabolic PDEs, rather than by pure delay. Replete with examples, Delay Compensation for Nonlinear, Adaptive, and PDE Systems is an excellent reference guide for graduate students, researchers, and professionals in mathematics, systems control, as well as chemical, mechanical, electrical, computer, aerospace, and civil/structural engineering. Parts of the book may be used in graduate courses on general distributed parameter systems, linear delay systems, PDEs, nonlinear control, state estimator and observers, adaptive control, robust control, or linear time-varying systems.