Differential Equations And Control Theory

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Control Theory Tutorial

Author : Steven A. Frank
Publisher : Springer
Page : 112 pages
File Size : 47,5 Mb
Release : 2018-05-29
Category : Technology & Engineering
ISBN : 9783319917078

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Control Theory Tutorial by Steven A. Frank Pdf

This open access Brief introduces the basic principles of control theory in a concise self-study guide. It complements the classic texts by emphasizing the simple conceptual unity of the subject. A novice can quickly see how and why the different parts fit together. The concepts build slowly and naturally one after another, until the reader soon has a view of the whole. Each concept is illustrated by detailed examples and graphics. The full software code for each example is available, providing the basis for experimenting with various assumptions, learning how to write programs for control analysis, and setting the stage for future research projects. The topics focus on robustness, design trade-offs, and optimality. Most of the book develops classical linear theory. The last part of the book considers robustness with respect to nonlinearity and explicitly nonlinear extensions, as well as advanced topics such as adaptive control and model predictive control. New students, as well as scientists from other backgrounds who want a concise and easy-to-grasp coverage of control theory, will benefit from the emphasis on concepts and broad understanding of the various approaches. Electronic codes for this title can be downloaded from https://extras.springer.com/?query=978-3-319-91707-8

Recent Advances in Differential Equations and Control Theory

Author : Concepción Muriel,Carmen Pérez-Martinez
Publisher : Springer Nature
Page : 102 pages
File Size : 47,9 Mb
Release : 2021-03-13
Category : Mathematics
ISBN : 9783030618759

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Recent Advances in Differential Equations and Control Theory by Concepción Muriel,Carmen Pérez-Martinez Pdf

This book collects the latest results and new trends in the application of mathematics to some problems in control theory, numerical simulation and differential equations. The work comprises the main results presented at a thematic minisymposium, part of the 9th International Congress on Industrial and Applied Mathematics (ICIAM 2019), held in Valencia, Spain, from 15 to 18 July 2019. The topics covered in the 6 peer-review contributions involve applications of numerical methods to real problems in oceanography and naval engineering, as well as relevant results on switching control techniques, which can have multiple applications in industrial complexes, electromechanical machines, biological systems, etc. Problems in control theory, as in most engineering problems, are modeled by differential equations, for which standard solving procedures may be insufficient. The book also includes recent geometric and analytical methods for the search of exact solutions for differential equations, which serve as essential tools for analyzing problems in many scientific disciplines.

Mathematical Control Theory for Stochastic Partial Differential Equations

Author : Qi Lü,Xu Zhang
Publisher : Springer
Page : 0 pages
File Size : 46,9 Mb
Release : 2022-09-18
Category : Science
ISBN : 3030823334

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Mathematical Control Theory for Stochastic Partial Differential Equations by Qi Lü,Xu Zhang Pdf

This is the first book to systematically present control theory for stochastic distributed parameter systems, a comparatively new branch of mathematical control theory. The new phenomena and difficulties arising in the study of controllability and optimal control problems for this type of system are explained in detail. Interestingly enough, one has to develop new mathematical tools to solve some problems in this field, such as the global Carleman estimate for stochastic partial differential equations and the stochastic transposition method for backward stochastic evolution equations. In a certain sense, the stochastic distributed parameter control system is the most general control system in the context of classical physics. Accordingly, studying this field may also yield valuable insights into quantum control systems. A basic grasp of functional analysis, partial differential equations, and control theory for deterministic systems is the only prerequisite for reading this book.

Trends in Control Theory and Partial Differential Equations

Author : Fatiha Alabau-Boussouira,Fabio Ancona,Alessio Porretta,Carlo Sinestrari
Publisher : Springer
Page : 276 pages
File Size : 49,8 Mb
Release : 2019-07-04
Category : Mathematics
ISBN : 9783030179496

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Trends in Control Theory and Partial Differential Equations by Fatiha Alabau-Boussouira,Fabio Ancona,Alessio Porretta,Carlo Sinestrari Pdf

This book presents cutting-edge contributions in the areas of control theory and partial differential equations. Over the decades, control theory has had deep and fruitful interactions with the theory of partial differential equations (PDEs). Well-known examples are the study of the generalized solutions of Hamilton-Jacobi-Bellman equations arising in deterministic and stochastic optimal control and the development of modern analytical tools to study the controllability of infinite dimensional systems governed by PDEs. In the present volume, leading experts provide an up-to-date overview of the connections between these two vast fields of mathematics. Topics addressed include regularity of the value function associated to finite dimensional control systems, controllability and observability for PDEs, and asymptotic analysis of multiagent systems. The book will be of interest for both researchers and graduate students working in these areas.

Control Theory for Partial Differential Equations: Volume 1, Abstract Parabolic Systems

Author : Irena Lasiecka,Roberto Triggiani
Publisher : Cambridge University Press
Page : 678 pages
File Size : 40,5 Mb
Release : 2000-02-13
Category : Mathematics
ISBN : 0521434084

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Control Theory for Partial Differential Equations: Volume 1, Abstract Parabolic Systems by Irena Lasiecka,Roberto Triggiani Pdf

First of a two-volume treatise on deterministic control systems modeled by multi-dimensional partial differential equations, originally published in 2000.

Control Theory of Systems Governed by Partial Differential Equations

Author : A.K. Aziz,J.W. Wingate,M.J. Balas
Publisher : Academic Press
Page : 288 pages
File Size : 48,6 Mb
Release : 2014-05-10
Category : Technology & Engineering
ISBN : 9781483216300

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Control Theory of Systems Governed by Partial Differential Equations by A.K. Aziz,J.W. Wingate,M.J. Balas Pdf

Control Theory of Systems Governed by Partial Differential Equations covers the proceedings of the 1976 Conference by the same title, held at the Naval Surface Weapons Center, Silver Spring, Maryland. The purpose of this conference is to examine the control theory of partial differential equations and its application. This text is divided into five chapters that primarily focus on tutorial lecture series on the theory of optimal control of distributed systems. It describes the many manifestations of the theory and its applications appearing in the other chapters. This work also presents the principles of the duality and asymptotic methods in control theory, including the variational principle for the heat equation. A chapter highlights systems that are not of the linear quadratic type. This chapter also explores the control of free surfaces and the geometrical control variables. The last chapter provides a summary of the features and applications of the numerical approximation of problems of optimal control. This book will prove useful to mathematicians, engineers, and researchers.

Mathematical Control Theory for Stochastic Partial Differential Equations

Author : Qi Lü,Xu Zhang
Publisher : Springer Nature
Page : 592 pages
File Size : 48,7 Mb
Release : 2021-10-19
Category : Science
ISBN : 9783030823313

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Mathematical Control Theory for Stochastic Partial Differential Equations by Qi Lü,Xu Zhang Pdf

This is the first book to systematically present control theory for stochastic distributed parameter systems, a comparatively new branch of mathematical control theory. The new phenomena and difficulties arising in the study of controllability and optimal control problems for this type of system are explained in detail. Interestingly enough, one has to develop new mathematical tools to solve some problems in this field, such as the global Carleman estimate for stochastic partial differential equations and the stochastic transposition method for backward stochastic evolution equations. In a certain sense, the stochastic distributed parameter control system is the most general control system in the context of classical physics. Accordingly, studying this field may also yield valuable insights into quantum control systems. A basic grasp of functional analysis, partial differential equations, and control theory for deterministic systems is the only prerequisite for reading this book.

Control Theory of Partial Differential Equations

Author : Guenter Leugering,Oleg Imanuvilov,Bing-Yu Zhang,Roberto Triggiani
Publisher : CRC Press
Page : 416 pages
File Size : 45,6 Mb
Release : 2005-05-27
Category : Mathematics
ISBN : 9781420028317

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Control Theory of Partial Differential Equations by Guenter Leugering,Oleg Imanuvilov,Bing-Yu Zhang,Roberto Triggiani Pdf

The field of control theory in PDEs has broadened considerably as more realistic models have been introduced and investigated. This book presents a broad range of recent developments, new discoveries, and mathematical tools in the field. The authors discuss topics such as elasticity, thermo-elasticity, aero-elasticity, interactions between fluids a

Differential Equations and Control Theory

Author : Z. Deng,Z. Liang,G. Lu,S. Ruan
Publisher : CRC Press
Page : 546 pages
File Size : 40,8 Mb
Release : 2020-11-25
Category : Mathematics
ISBN : 9781000148534

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Differential Equations and Control Theory by Z. Deng,Z. Liang,G. Lu,S. Ruan Pdf

This work presents the proceedings from the International Conference on Differential Equations and Control Theory, held recently in Wuhan, China. It provides an overview of current developments in a range of topics including dynamical systems, optimal control theory, stochastic control, chaos, fractals, wavelets and ordinary, partial, functional and stochastic differential equations.

Optimal Control of Partial Differential Equations

Author : Fredi Tröltzsch
Publisher : American Mathematical Society
Page : 417 pages
File Size : 49,7 Mb
Release : 2024-03-21
Category : Mathematics
ISBN : 9781470476441

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Optimal Control of Partial Differential Equations by Fredi Tröltzsch Pdf

Optimal control theory is concerned with finding control functions that minimize cost functions for systems described by differential equations. The methods have found widespread applications in aeronautics, mechanical engineering, the life sciences, and many other disciplines. This book focuses on optimal control problems where the state equation is an elliptic or parabolic partial differential equation. Included are topics such as the existence of optimal solutions, necessary optimality conditions and adjoint equations, second-order sufficient conditions, and main principles of selected numerical techniques. It also contains a survey on the Karush-Kuhn-Tucker theory of nonlinear programming in Banach spaces. The exposition begins with control problems with linear equations, quadratic cost functions and control constraints. To make the book self-contained, basic facts on weak solutions of elliptic and parabolic equations are introduced. Principles of functional analysis are introduced and explained as they are needed. Many simple examples illustrate the theory and its hidden difficulties. This start to the book makes it fairly self-contained and suitable for advanced undergraduates or beginning graduate students. Advanced control problems for nonlinear partial differential equations are also discussed. As prerequisites, results on boundedness and continuity of solutions to semilinear elliptic and parabolic equations are addressed. These topics are not yet readily available in books on PDEs, making the exposition also interesting for researchers. Alongside the main theme of the analysis of problems of optimal control, Tröltzsch also discusses numerical techniques. The exposition is confined to brief introductions into the basic ideas in order to give the reader an impression of how the theory can be realized numerically. After reading this book, the reader will be familiar with the main principles of the numerical analysis of PDE-constrained optimization.

Ordinary Differential Equations

Author : Hartmut Logemann,Eugene P. Ryan
Publisher : Springer
Page : 333 pages
File Size : 50,6 Mb
Release : 2014-07-08
Category : Mathematics
ISBN : 9781447163985

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Ordinary Differential Equations by Hartmut Logemann,Eugene P. Ryan Pdf

The book comprises a rigorous and self-contained treatment of initial-value problems for ordinary differential equations. It additionally develops the basics of control theory, which is a unique feature in current textbook literature. The following topics are particularly emphasised: • existence, uniqueness and continuation of solutions, • continuous dependence on initial data, • flows, • qualitative behaviour of solutions, • limit sets, • stability theory, • invariance principles, • introductory control theory, • feedback and stabilization. The last two items cover classical control theoretic material such as linear control theory and absolute stability of nonlinear feedback systems. It also includes an introduction to the more recent concept of input-to-state stability. Only a basic grounding in linear algebra and analysis is assumed. Ordinary Differential Equations will be suitable for final year undergraduate students of mathematics and appropriate for beginning postgraduates in mathematics and in mathematically oriented engineering and science.

Generalized Ordinary Differential Equations in Abstract Spaces and Applications

Author : Everaldo M. Bonotto,Márcia Federson,Jaqueline G. Mesquita
Publisher : John Wiley & Sons
Page : 514 pages
File Size : 55,5 Mb
Release : 2021-09-15
Category : Mathematics
ISBN : 9781119654933

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Generalized Ordinary Differential Equations in Abstract Spaces and Applications by Everaldo M. Bonotto,Márcia Federson,Jaqueline G. Mesquita Pdf

GENERALIZED ORDINARY DIFFERENTIAL EQUATIONS IN ABSTRACT SPACES AND APPLICATIONS Explore a unified view of differential equations through the use of the generalized ODE from leading academics in mathematics Generalized Ordinary Differential Equations in Abstract Spaces and Applications delivers a comprehensive treatment of new results of the theory of Generalized ODEs in abstract spaces. The book covers applications to other types of differential equations, including Measure Functional Differential Equations (measure FDEs). It presents a uniform collection of qualitative results of Generalized ODEs and offers readers an introduction to several theories, including ordinary differential equations, impulsive differential equations, functional differential equations, dynamical equations on time scales, and more. Throughout the book, the focus is on qualitative theory and on corresponding results for other types of differential equations, as well as the connection between Generalized Ordinary Differential Equations and impulsive differential equations, functional differential equations, measure differential equations and dynamic equations on time scales. The book’s descriptions will be of use in many mathematical contexts, as well as in the social and natural sciences. Readers will also benefit from the inclusion of: A thorough introduction to regulated functions, including their basic properties, equiregulated sets, uniform convergence, and relatively compact sets An exploration of the Kurzweil integral, including its definitions and basic properties A discussion of measure functional differential equations, including impulsive measure FDEs The interrelationship between generalized ODEs and measure FDEs A treatment of the basic properties of generalized ODEs, including the existence and uniqueness of solutions, and prolongation and maximal solutions Perfect for researchers and graduate students in Differential Equations and Dynamical Systems, Generalized Ordinary Differential Equations in Abstract Spaces and App­lications will also earn a place in the libraries of advanced undergraduate students taking courses in the subject and hoping to move onto graduate studies.

Matrix Riccati Equations in Control and Systems Theory

Author : Hisham Abou-Kandil,Gerhard Freiling,Vlad Ionescu,Gerhard Jank
Publisher : Birkhäuser
Page : 584 pages
File Size : 48,5 Mb
Release : 2012-12-06
Category : Science
ISBN : 9783034880817

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Matrix Riccati Equations in Control and Systems Theory by Hisham Abou-Kandil,Gerhard Freiling,Vlad Ionescu,Gerhard Jank Pdf

The authors present the theory of symmetric (Hermitian) matrix Riccati equations and contribute to the development of the theory of non-symmetric Riccati equations as well as to certain classes of coupled and generalized Riccati equations occurring in differential games and stochastic control. The volume offers a complete treatment of generalized and coupled Riccati equations. It deals with differential, discrete-time, algebraic or periodic symmetric and non-symmetric equations, with special emphasis on those equations appearing in control and systems theory. Extensions to Riccati theory allow to tackle robust control problems in a unified approach. The book makes available classical and recent results to engineers and mathematicians alike. It is accessible to graduate students in mathematics, applied mathematics, control engineering, physics or economics. Researchers working in any of the fields where Riccati equations are used can find the main results with the proper mathematical background.

Mathematical Control of Coupled PDEs

Author : Irena Lasiecka
Publisher : SIAM
Page : 248 pages
File Size : 54,9 Mb
Release : 2002-01-01
Category : Mathematics
ISBN : 9780898714869

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Mathematical Control of Coupled PDEs by Irena Lasiecka Pdf

Concentrates on systems of hyperbolic and parabolic coupled PDEs that are nonlinear, solve three key problems.

Control Theory for Partial Differential Equations: Volume 2, Abstract Hyperbolic-Like Systems Over a Finite Time Horizon

Author : Irena Lasiecka,Roberto Triggiani
Publisher : Unknown
Page : 128 pages
File Size : 47,6 Mb
Release : 2014-02-20
Category : Electronic
ISBN : 1299748929

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Control Theory for Partial Differential Equations: Volume 2, Abstract Hyperbolic-Like Systems Over a Finite Time Horizon by Irena Lasiecka,Roberto Triggiani Pdf

Second of a two-volume treatise on deterministic control systems modeled by multi-dimensional partial differential equations.