Theory Of Control Systems Described By Differential Inclusions

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Theory of Control Systems Described by Differential Inclusions

Zhengzhi Han,Xiushan Cai,Jun Huang
Theory of Control Systems Described by Differential Inclusions Book PDF

Author : Zhengzhi Han,Xiushan Cai,Jun Huang
Publisher : Springer
Page : 0 pages
File Size : 54,7 Mb
Release : 2018-06-07
Category : Technology & Engineering
ISBN : 3662569930

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Theory of Control Systems Described by Differential Inclusions by Zhengzhi Han,Xiushan Cai,Jun Huang Pdf

This book provides a brief introduction to the theory of finite dimensional differential inclusions, and deals in depth with control of three kinds of differential inclusion systems. The authors introduce the algebraic decomposition of convex processes, the stabilization of polytopic systems, and observations of Luré systems. They also introduce the elemental theory of finite dimensional differential inclusions, and the properties and designs of the control systems described by differential inclusions. Addressing the material with clarity and simplicity, the book includes recent research achievements and spans all concepts, concluding with a critical mathematical framework. This book is intended for researchers, teachers and postgraduate students in the area of automatic control engineering.

Theory of Control Systems Described by Differential Inclusions

Zhengzhi Han,Xiushan Cai,Jun Huang
Theory of Control Systems Described by Differential Inclusions Book PDF

Author : Zhengzhi Han,Xiushan Cai,Jun Huang
Publisher : Springer
Page : 344 pages
File Size : 43,6 Mb
Release : 2016-06-15
Category : Technology & Engineering
ISBN : 9783662492451

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Theory of Control Systems Described by Differential Inclusions by Zhengzhi Han,Xiushan Cai,Jun Huang Pdf

This book provides a brief introduction to the theory of finite dimensional differential inclusions, and deals in depth with control of three kinds of differential inclusion systems. The authors introduce the algebraic decomposition of convex processes, the stabilization of polytopic systems, and observations of Luré systems. They also introduce the elemental theory of finite dimensional differential inclusions, and the properties and designs of the control systems described by differential inclusions. Addressing the material with clarity and simplicity, the book includes recent research achievements and spans all concepts, concluding with a critical mathematical framework. This book is intended for researchers, teachers and postgraduate students in the area of automatic control engineering.

Introduction to the Theory of Differential Inclusions

Georgi V. Smirnov
Introduction to the Theory of Differential Inclusions Book PDF

Author : Georgi V. Smirnov
Publisher : American Mathematical Society
Page : 226 pages
File Size : 52,8 Mb
Release : 2022-02-22
Category : Mathematics
ISBN : 9781470468545

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Introduction to the Theory of Differential Inclusions by Georgi V. Smirnov Pdf

A differential inclusion is a relation of the form $dot x in F(x)$, where $F$ is a set-valued map associating any point $x in R^n$ with a set $F(x) subset R^n$. As such, the notion of a differential inclusion generalizes the notion of an ordinary differential equation of the form $dot x = f(x)$. Therefore, all problems usually studied in the theory of ordinary differential equations (existence and continuation of solutions, dependence on initial conditions and parameters, etc.) can be studied for differential inclusions as well. Since a differential inclusion usually has many solutions starting at a given point, new types of problems arise, such as investigation of topological properties of the set of solutions, selection of solutions with given properties, and many others. Differential inclusions play an important role as a tool in the study of various dynamical processes described by equations with a discontinuous or multivalued right-hand side, occurring, in particular, in the study of dynamics of economical, social, and biological macrosystems. They also are very useful in proving existence theorems in control theory. This text provides an introductory treatment to the theory of differential inclusions. The reader is only required to know ordinary differential equations, theory of functions, and functional analysis on the elementary level. Chapter 1 contains a brief introduction to convex analysis. Chapter 2 considers set-valued maps. Chapter 3 is devoted to the Mordukhovich version of nonsmooth analysis. Chapter 4 contains the main existence theorems and gives an idea of the approximation techniques used throughout the text. Chapter 5 is devoted to the viability problem, i.e., the problem of selection of a solution to a differential inclusion that is contained in a given set. Chapter 6 considers the controllability problem. Chapter 7 discusses extremal problems for differential inclusions. Chapter 8 presents stability theory, and Chapter 9 deals with the stabilization problem.

Approximation and Optimization of Discrete and Differential Inclusions

Elimhan N Mahmudov
Approximation and Optimization of Discrete and Differential Inclusions Book PDF

Author : Elimhan N Mahmudov
Publisher : Elsevier
Page : 396 pages
File Size : 45,8 Mb
Release : 2011-08-25
Category : Mathematics
ISBN : 9780123884282

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Approximation and Optimization of Discrete and Differential Inclusions by Elimhan N Mahmudov Pdf

Optimal control theory has numerous applications in both science and engineering. This book presents basic concepts and principles of mathematical programming in terms of set-valued analysis and develops a comprehensive optimality theory of problems described by ordinary and partial differential inclusions. In addition to including well-recognized results of variational analysis and optimization, the book includes a number of new and important ones Includes practical examples

Nonlinear Controllability and Optimal Control

Sussmann
Nonlinear Controllability and Optimal Control Book PDF

Author : Sussmann
Publisher : Routledge
Page : 277 pages
File Size : 43,6 Mb
Release : 2017-11-22
Category : Mathematics
ISBN : 9781351428323

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Nonlinear Controllability and Optimal Control by Sussmann Pdf

This outstanding reference presents current, state-of-the-art research on importantproblems of finite-dimensional nonlinear optimal control and controllability theory. Itpresents an overview of a broad variety of new techniques useful in solving classicalcontrol theory problems.Written and edited by renowned mathematicians at the forefront of research in thisevolving field, Nonlinear Controllability and Optimal Control providesdetailed coverage of the construction of solutions of differential inclusions by means ofdirectionally continuous sections ... Lie algebraic conditions for local controllability... the use of the Campbell-Hausdorff series to derive properties of optimal trajectories... the Fuller phenomenon ... the theory of orbits ... and more.Containing more than 1,300 display equations, this exemplary, instructive reference is aninvaluable source for mathematical researchers and applied mathematicians, electrical andelectronics, aerospace, mechanical, control, systems, and computer engineers, and graduatestudents in these disciplines .

Control Theory and its Applications

Roxin
Control Theory and its Applications Book PDF

Author : Roxin
Publisher : CRC Press
Page : 204 pages
File Size : 42,9 Mb
Release : 1997-01-23
Category : Technology & Engineering
ISBN : 2919875221

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Control Theory and its Applications by Roxin Pdf

The general context of this book is applied to systems in n-dimensional space. Emphasis is placed on a general approach to control theory, independent of optimization, and demonstrates a novel approach by converting a given dynamical system into a control system, in order to obtain a deeper understanding of its mode of action. Contents of the monograph include a presentation of the basic concepts and results of control theory, the typical and classical behaviour of control systems, techniques for transforming dynamic systems into control systems, and the systematic approach to study control systems in applications, as shown in many examples.

Differential Inclusions

J.-P. Aubin,A. Cellina
Differential Inclusions Book PDF

Author : J.-P. Aubin,A. Cellina
Publisher : Springer Science & Business Media
Page : 353 pages
File Size : 55,9 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9783642695124

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Differential Inclusions by J.-P. Aubin,A. Cellina Pdf

A great impetus to study differential inclusions came from the development of Control Theory, i.e. of dynamical systems x'(t) = f(t, x(t), u(t)), x(O)=xo "controlled" by parameters u(t) (the "controls"). Indeed, if we introduce the set-valued map F(t, x)= {f(t, x, u)}ueu then solutions to the differential equations (*) are solutions to the "differen tial inclusion" (**) x'(t)EF(t, x(t)), x(O)=xo in which the controls do not appear explicitely. Systems Theory provides dynamical systems of the form d x'(t)=A(x(t)) dt (B(x(t))+ C(x(t)); x(O)=xo in which the velocity of the state of the system depends not only upon the x(t) of the system at time t, but also on variations of observations state B(x(t)) of the state. This is a particular case of an implicit differential equation f(t, x(t), x'(t)) = 0 which can be regarded as a differential inclusion (**), where the right-hand side F is defined by F(t, x)= {vlf(t, x, v)=O}. During the 60's and 70's, a special class of differential inclusions was thoroughly investigated: those of the form X'(t)E - A(x(t)), x (0) =xo where A is a "maximal monotone" map. This class of inclusions contains the class of "gradient inclusions" which generalize the usual gradient equations x'(t) = -VV(x(t)), x(O)=xo when V is a differentiable "potential". 2 Introduction There are many instances when potential functions are not differentiable

Stochastic Differential Inclusions and Applications

Michał Kisielewicz
Stochastic Differential Inclusions and Applications Book PDF

Author : Michał Kisielewicz
Publisher : Springer Science & Business Media
Page : 295 pages
File Size : 50,6 Mb
Release : 2013-06-12
Category : Mathematics
ISBN : 9781461467564

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Stochastic Differential Inclusions and Applications by Michał Kisielewicz Pdf

​This book aims to further develop the theory of stochastic functional inclusions and their applications for describing the solutions of the initial and boundary value problems for partial differential inclusions. The self-contained volume is designed to introduce the reader in a systematic fashion, to new methods of the stochastic optimal control theory from the very beginning. The exposition contains detailed proofs and uses new and original methods to characterize the properties of stochastic functional inclusions that, up to the present time, have only been published recently by the author. The work is divided into seven chapters, with the first two acting as an introduction, containing selected material dealing with point- and set-valued stochastic processes, and the final two devoted to applications and optimal control problems. The book presents recent and pressing issues in stochastic processes, control, differential games, optimization and their application in finance, manufacturing, queueing networks, and climate control. Written by an award-winning author in the field of stochastic differential inclusions and their application to control theory, This book is intended for students and researchers in mathematics and applications; particularly those studying optimal control theory. It is also highly relevant for students of economics and engineering. The book can also be used as a reference on stochastic differential inclusions. Knowledge of select topics in analysis and probability theory are required.

Tautological Control Systems

Andrew D. Lewis
Tautological Control Systems Book PDF

Author : Andrew D. Lewis
Publisher : Springer
Page : 128 pages
File Size : 44,5 Mb
Release : 2014-07-22
Category : Science
ISBN : 9783319086385

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Tautological Control Systems by Andrew D. Lewis Pdf

This brief presents a description of a new modelling framework for nonlinear/geometric control theory. The framework is intended to be—and shown to be—feedback-invariant. As such, Tautological Control Systems provides a platform for understanding fundamental structural problems in geometric control theory. Part of the novelty of the text stems from the variety of regularity classes, e.g., Lipschitz, finitely differentiable, smooth, real analytic, with which it deals in a comprehensive and unified manner. The treatment of the important real analytic class especially reflects recent work on real analytic topologies by the author. Applied mathematicians interested in nonlinear and geometric control theory will find this brief of interest as a starting point for work in which feedback invariance is important. Graduate students working in control theory may also find Tautological Control Systems to be a stimulating starting point for their research.

Multivalued Maps And Differential Inclusions: Elements Of Theory And Applications

Valeri Obukhovskii,Boris Gel'man
Multivalued Maps And Differential Inclusions Elements Of Theory And Applications Book PDF

Author : Valeri Obukhovskii,Boris Gel'man
Publisher : World Scientific
Page : 221 pages
File Size : 44,7 Mb
Release : 2020-04-04
Category : Mathematics
ISBN : 9789811220234

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Multivalued Maps And Differential Inclusions: Elements Of Theory And Applications by Valeri Obukhovskii,Boris Gel'man Pdf

The theory of multivalued maps and the theory of differential inclusions are closely connected and intensively developing branches of contemporary mathematics. They have effective and interesting applications in control theory, optimization, calculus of variations, non-smooth and convex analysis, game theory, mathematical economics and in other fields.This book presents a user-friendly and self-contained introduction to both subjects. It is aimed at 'beginners', starting with students of senior courses. The book will be useful both for readers whose interests lie in the sphere of pure mathematics, as well as for those who are involved in applicable aspects of the theory. In Chapter 0, basic definitions and fundamental results in topology are collected. Chapter 1 begins with examples showing how naturally the idea of a multivalued map arises in diverse areas of mathematics, continues with the description of a variety of properties of multivalued maps and finishes with measurable multivalued functions. Chapter 2 is devoted to the theory of fixed points of multivalued maps. The whole of Chapter 3 focuses on the study of differential inclusions and their applications in control theory. The subject of last Chapter 4 is the applications in dynamical systems, game theory, and mathematical economics.The book is completed with the bibliographic commentaries and additions containing the exposition related both to the sections described in the book and to those which left outside its framework. The extensive bibliography (including more than 400 items) leads from basic works to recent studies.

Control Theory of Systems Governed by Partial Differential Equations

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

Author : A.K. Aziz,J.W. Wingate,M.J. Balas
Publisher : Academic Press
Page : 289 pages
File Size : 40,8 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.

Topological Methods for Differential Equations and Inclusions

John R. Graef,Johnny Henderson,Abdelghani Ouahab
Topological Methods for Differential Equations and Inclusions Book PDF

Author : John R. Graef,Johnny Henderson,Abdelghani Ouahab
Publisher : CRC Press
Page : 430 pages
File Size : 40,8 Mb
Release : 2018-09-25
Category : Mathematics
ISBN : 9780429822612

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Topological Methods for Differential Equations and Inclusions by John R. Graef,Johnny Henderson,Abdelghani Ouahab Pdf

Topological Methods for Differential Equations and Inclusions covers the important topics involving topological methods in the theory of systems of differential equations. The equivalence between a control system and the corresponding differential inclusion is the central idea used to prove existence theorems in optimal control theory. Since the dynamics of economic, social, and biological systems are multi-valued, differential inclusions serve as natural models in macro systems with hysteresis.

Control Theory

J.R. Leigh
Control Theory Book PDF

Author : J.R. Leigh
Publisher : IET
Page : 321 pages
File Size : 41,7 Mb
Release : 2004
Category : Technology & Engineering
ISBN : 9780863413391

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Control Theory by J.R. Leigh Pdf

For students or professionals in science, math, or industry--with or without a background in control theory--explains and illustrates the basic concepts underlying the theory, with references to more detailed treatments. Intended as a companion to more traditional approaches, begins with simple concepts such as feedback and stability, and advances to optimization, distributed parameter systems, and other complex ideas. Annotation copyrighted by Book News, Inc., Portland, OR

Numerical Software Verification

Majid Zamani,Damien Zufferey
Numerical Software Verification Book PDF

Author : Majid Zamani,Damien Zufferey
Publisher : Springer
Page : 145 pages
File Size : 47,7 Mb
Release : 2019-08-02
Category : Computers
ISBN : 9783030284237

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Numerical Software Verification by Majid Zamani,Damien Zufferey Pdf

This book constitutes the proceedings of the 12th International Workshop on Numerical Software Verification, NSV 2019, held in New York City, NY, USA, in July 2019 - colocated with the International Conference on Computer Aided Verification, CAV 2019. The 5 full papers presented together with 2 short papers, 3 abstracts of invited talks, and 2 tutorial papers were carefully reviewed and selected from numerous submissions. The NSV 2017 workshop is dedicated to the development of logical and mathematical techniques for the reasoning about programmability and reliability.

New Trends in Systems Theory

Giuseppe Conte,Anna M. Perdon,Bostwick Wyman
New Trends in Systems Theory Book PDF

Author : Giuseppe Conte,Anna M. Perdon,Bostwick Wyman
Publisher : Springer Science & Business Media
Page : 741 pages
File Size : 54,7 Mb
Release : 2013-03-07
Category : Science
ISBN : 9781461204398

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New Trends in Systems Theory by Giuseppe Conte,Anna M. Perdon,Bostwick Wyman Pdf

The University of Genoa - Ohio State University Joint Conference on New Trends in Systems Theory was held at the Badia di S. Andrea in Genoa on July 9-11, 1990. This Proceedings volume contains articles based on two of the three Plenary talks and most of the shorter presentations. The papers are arranged by author, and no attempt has been made to organize them by topic. We would like to thank the members of the Scientific Committee and of the Program Committee, the speakers and authors, and everyone who attended the conference. Approximately 120 researchers and students from all over the world visited Genoa for the meeting, representing a wide spectrum of areas in pure and applied control and systems theory. The success of the conference depended on their high level of scientific and engineering expertise, not to mention their enthusiasm. The Conference on New Trends in Systems Theory would not have been possible without the help of a great many institutions and people. We would like to thank the University of Genoa, particularly Professor Enrico Beltrametti, and the Ohio State University's Columbian Quincentenary Committee led by Professor Christian Zacher, for encouragement and financial assistance. The University of Genoa Mathematics Department and Communication, Computer and System Sciences Department supplied assistance and technical help. The staff of the Consorzio Genova Ricerche, particularly Ms. Piera Ponta and Ms. Camilla Marconi, worked diligently over many months and especially during the conference itself to insure a smooth and enjoyable meeting.