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Control In Finite And Infinite Dimension
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Book Synopsis Infinite Dimensional Optimization and Control Theory by : Hector O. Fattorini
Download or read book Infinite Dimensional Optimization and Control Theory written by Hector O. Fattorini and published by Cambridge University Press. This book was released on 1999-03-28 with total page 828 pages. Available in PDF, EPUB and Kindle. Book excerpt: Treats optimal problems for systems described by ODEs and PDEs, using an approach that unifies finite and infinite dimensional nonlinear programming.
Book Synopsis Stochastic Optimal Control in Infinite Dimension by : Giorgio Fabbri
Download or read book Stochastic Optimal Control in Infinite Dimension written by Giorgio Fabbri and published by Springer. This book was released on 2017-06-22 with total page 928 pages. Available in PDF, EPUB and Kindle. Book excerpt: Providing an introduction to stochastic optimal control in infinite dimension, this book gives a complete account of the theory of second-order HJB equations in infinite-dimensional Hilbert spaces, focusing on its applicability to associated stochastic optimal control problems. It features a general introduction to optimal stochastic control, including basic results (e.g. the dynamic programming principle) with proofs, and provides examples of applications. A complete and up-to-date exposition of the existing theory of viscosity solutions and regular solutions of second-order HJB equations in Hilbert spaces is given, together with an extensive survey of other methods, with a full bibliography. In particular, Chapter 6, written by M. Fuhrman and G. Tessitore, surveys the theory of regular solutions of HJB equations arising in infinite-dimensional stochastic control, via BSDEs. The book is of interest to both pure and applied researchers working in the control theory of stochastic PDEs, and in PDEs in infinite dimension. Readers from other fields who want to learn the basic theory will also find it useful. The prerequisites are: standard functional analysis, the theory of semigroups of operators and its use in the study of PDEs, some knowledge of the dynamic programming approach to stochastic optimal control problems in finite dimension, and the basics of stochastic analysis and stochastic equations in infinite-dimensional spaces.
Book Synopsis Optimal Control Theory for Infinite Dimensional Systems by : Xungjing Li
Download or read book Optimal Control Theory for Infinite Dimensional Systems written by Xungjing Li and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 462 pages. Available in PDF, EPUB and Kindle. Book excerpt: Infinite dimensional systems can be used to describe many phenomena in the real world. As is well known, heat conduction, properties of elastic plastic material, fluid dynamics, diffusion-reaction processes, etc., all lie within this area. The object that we are studying (temperature, displace ment, concentration, velocity, etc.) is usually referred to as the state. We are interested in the case where the state satisfies proper differential equa tions that are derived from certain physical laws, such as Newton's law, Fourier's law etc. The space in which the state exists is called the state space, and the equation that the state satisfies is called the state equation. By an infinite dimensional system we mean one whose corresponding state space is infinite dimensional. In particular, we are interested in the case where the state equation is one of the following types: partial differential equation, functional differential equation, integro-differential equation, or abstract evolution equation. The case in which the state equation is being a stochastic differential equation is also an infinite dimensional problem, but we will not discuss such a case in this book.
Book Synopsis Infinite Dimensional And Finite Dimensional Stochastic Equations And Applications In Physics by : Wilfried Grecksch
Download or read book Infinite Dimensional And Finite Dimensional Stochastic Equations And Applications In Physics written by Wilfried Grecksch and published by World Scientific. This book was released on 2020-04-22 with total page 261 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains survey articles on various aspects of stochastic partial differential equations (SPDEs) and their applications in stochastic control theory and in physics.The topics presented in this volume are:This book is intended not only for graduate students in mathematics or physics, but also for mathematicians, mathematical physicists, theoretical physicists, and science researchers interested in the physical applications of the theory of stochastic processes.
Book Synopsis An Introduction to Infinite-Dimensional Linear Systems Theory by : Ruth F. Curtain
Download or read book An Introduction to Infinite-Dimensional Linear Systems Theory written by Ruth F. Curtain and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 714 pages. Available in PDF, EPUB and Kindle. Book excerpt: Infinite dimensional systems is now an established area of research. Given the recent trend in systems theory and in applications towards a synthesis of time- and frequency-domain methods, there is a need for an introductory text which treats both state-space and frequency-domain aspects in an integrated fashion. The authors' primary aim is to write an introductory textbook for a course on infinite dimensional linear systems. An important consideration by the authors is that their book should be accessible to graduate engineers and mathematicians with a minimal background in functional analysis. Consequently, all the mathematical background is summarized in an extensive appendix. For the majority of students, this would be their only acquaintance with infinite dimensional systems.
Book Synopsis Mathematical Control Theory by : Eduardo D. Sontag
Download or read book Mathematical Control Theory written by Eduardo D. Sontag and published by Springer Science & Business Media. This book was released on 2013-11-21 with total page 543 pages. Available in PDF, EPUB and Kindle. Book excerpt: Geared primarily to an audience consisting of mathematically advanced undergraduate or beginning graduate students, this text may additionally be used by engineering students interested in a rigorous, proof-oriented systems course that goes beyond the classical frequency-domain material and more applied courses. The minimal mathematical background required is a working knowledge of linear algebra and differential equations. The book covers what constitutes the common core of control theory and is unique in its emphasis on foundational aspects. While covering a wide range of topics written in a standard theorem/proof style, it also develops the necessary techniques from scratch. In this second edition, new chapters and sections have been added, dealing with time optimal control of linear systems, variational and numerical approaches to nonlinear control, nonlinear controllability via Lie-algebraic methods, and controllability of recurrent nets and of linear systems with bounded controls.
Book Synopsis Infinite Dimensional Linear Control Systems by :
Download or read book Infinite Dimensional Linear Control Systems written by and published by Elsevier. This book was released on 2005-07-12 with total page 332 pages. Available in PDF, EPUB and Kindle. Book excerpt: For more than forty years, the equation y'(t) = Ay(t) + u(t) in Banach spaces has been used as model for optimal control processes described by partial differential equations, in particular heat and diffusion processes. Many of the outstanding open problems, however, have remained open until recently, and some have never been solved. This book is a survey of all results know to the author, with emphasis on very recent results (1999 to date). The book is restricted to linear equations and two particular problems (the time optimal problem, the norm optimal problem) which results in a more focused and concrete treatment. As experience shows, results on linear equations are the basis for the treatment of their semilinear counterparts, and techniques for the time and norm optimal problems can often be generalized to more general cost functionals. The main object of this book is to be a state-of-the-art monograph on the theory of the time and norm optimal controls for y'(t) = Ay(t) + u(t) that ends at the very latest frontier of research, with open problems and indications for future research. Key features: · Applications to optimal diffusion processes. · Applications to optimal heat propagation processes. · Modelling of optimal processes governed by partial differential equations. · Complete bibliography. · Includes the latest research on the subject. · Does not assume anything from the reader except basic functional analysis. · Accessible to researchers and advanced graduate students alike· Applications to optimal diffusion processes.· Applications to optimal heat propagation processes.· Modelling of optimal processes governed by partial differential equations.· Complete bibliography.· Includes the latest research on the subject.· Does not assume anything from the reader except basic functional analysis.· Accessible to researchers and advanced graduate students alike
Book Synopsis Mathematical Control Theory I by : M. Kanat Camlibel
Download or read book Mathematical Control Theory I written by M. Kanat Camlibel and published by Springer. This book was released on 2015-07-15 with total page 407 pages. Available in PDF, EPUB and Kindle. Book excerpt: This treatment of modern topics related to mathematical systems theory forms the proceedings of a workshop, Mathematical Systems Theory: From Behaviors to Nonlinear Control, held at the University of Groningen in July 2015. The workshop celebrated the work of Professors Arjan van der Schaft and Harry Trentelman, honouring their 60th Birthdays. The first volume of this two-volume work covers a variety of topics related to nonlinear and hybrid control systems. After giving a detailed account of the state of the art in the related topic, each chapter presents new results and discusses new directions. As such, this volume provides a broad picture of the theory of nonlinear and hybrid control systems for scientists and engineers with an interest in the interdisciplinary field of systems and control theory. The reader will benefit from the expert participants’ ideas on exciting new approaches to control and system theory and their predictions of future directions for the subject that were discussed at the workshop.
Book Synopsis Stochastic Equations in Infinite Dimensions by : Da Prato Guiseppe
Download or read book Stochastic Equations in Infinite Dimensions written by Da Prato Guiseppe and published by . This book was released on 2013-11-21 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: The aim of this book is to give a systematic and self-contained presentation of basic results on stochastic evolution equations in infinite dimensional, typically Hilbert and Banach, spaces. These are a generalization of stochastic differential equations as introduced by Ito and Gikham that occur, for instance, when describing random phenomena that crop up in science and engineering, as well as in the study of differential equations. The book is divided into three parts. In the first the authors give a self-contained exposition of the basic properties of probability measure on separable Banach and Hilbert spaces, as required later; they assume a reasonable background in probability theory and finite dimensional stochastic processes. The second part is devoted to the existence and uniqueness of solutions of a general stochastic evolution equation, and the third concerns the qualitative properties of those solutions. Appendices gather together background results from analysis that are otherwise hard to find under one roof. The book ends with a comprehensive bibliography that will contribute to the book's value for all working in stochastic differential equations."
Book Synopsis Handbook of Differential Equations: Evolutionary Equations by : C.M. Dafermos
Download or read book Handbook of Differential Equations: Evolutionary Equations written by C.M. Dafermos and published by Elsevier. This book was released on 2011-09-22 with total page 653 pages. Available in PDF, EPUB and Kindle. Book excerpt: The material collected in this volume reflects the active present of this area of mathematics, ranging from the abstract theory of gradient flows to stochastic representations of non-linear parabolic PDE's.Articles will highlight the present as well as expected future directions of development of the field with particular emphasis on applications. The article by Ambrosio and Savaré discussesthe most recent development in the theory of gradient flow of probability measures. After an introduction reviewing the properties of the Wasserstein space and corresponding subdifferential calculus, applications are given to evolutionarypartial differential equations. The contribution of Herrero provides a description of some mathematical approaches developed to account for quantitative as well as qualitative aspects of chemotaxis. Particular attention is paid to the limits of cell'scapability to measure external cues on the one hand, and to provide an overall description of aggregation models for the slim mold Dictyostelium discoideum on the other.The chapter written by Masmoudi deals with a rather different topic - examples of singular limits in hydrodynamics. This is nowadays a well-studied issue given the amount of new results based on the development of the existence theory for rather general systems of equations in hydrodynamics. The paper by DeLellis addreses the most recent results for the transport equations with regard to possible applications in the theory of hyperbolic systems of conservation laws. Emphasis is put on the development of the theory in the case when the governing field is only a BV function.The chapter by Rein represents a comprehensive survey of results on the Poisson-Vlasov system in astrophysics. The question of global stability of steady states is addressed in detail. The contribution of Soner is devoted to different representations of non-linear parabolic equations in terms of Markov processes. After a brief introduction on the linear theory, a class ofnon-linear equations is investigated, with applications to stochastic control and differential games.The chapter written by Zuazua presents some of the recent progresses done on the problem of controllabilty of partial differential equations. The applications include the linear wave and heat equations,parabolic equations with coefficients of low regularity, and some fluid-structure interaction models.- Volume 1 focuses on the abstract theory of evolution- Volume 2 considers more concrete probelms relating to specific applications- Volume 3 reflects the active present of this area of mathematics, ranging from the abstract theory of gradient flows to stochastic representations of non-linear PDEs
Book Synopsis Mathematical Control Theory by : Jerzy Zabczyk
Download or read book Mathematical Control Theory written by Jerzy Zabczyk and published by Springer Science & Business Media. This book was released on 2008 with total page 276 pages. Available in PDF, EPUB and Kindle. Book excerpt: In a mathematically precise manner, this book presents a unified introduction to deterministic control theory. It includes material on the realization of both linear and nonlinear systems, impulsive control, and positive linear systems.
Book Synopsis Finite and Infinite Games by : James Carse
Download or read book Finite and Infinite Games written by James Carse and published by Simon and Schuster. This book was released on 2011-10-11 with total page 155 pages. Available in PDF, EPUB and Kindle. Book excerpt: “There are at least two kinds of games,” states James P. Carse as he begins this extraordinary book. “One could be called finite; the other infinite. A finite game is played for the purpose of winning, an infinite game for the purpose of continuing the play.” Finite games are the familiar contests of everyday life; they are played in order to be won, which is when they end. But infinite games are more mysterious. Their object is not winning, but ensuring the continuation of play. The rules may change, the boundaries may change, even the participants may change—as long as the game is never allowed to come to an end. What are infinite games? How do they affect the ways we play our finite games? What are we doing when we play—finitely or infinitely? And how can infinite games affect the ways in which we live our lives? Carse explores these questions with stunning elegance, teasing out of his distinctions a universe of observation and insight, noting where and why and how we play, finitely and infinitely. He surveys our world—from the finite games of the playing field and playing board to the infinite games found in culture and religion—leaving all we think we know illuminated and transformed. Along the way, Carse finds new ways of understanding everything, from how an actress portrays a role to how we engage in sex, from the nature of evil to the nature of science. Finite games, he shows, may offer wealth and status, power and glory, but infinite games offer something far more subtle and far grander. Carse has written a book rich in insight and aphorism. Already an international literary event, Finite and Infinite Games is certain to be argued about and celebrated for years to come. Reading it is the first step in learning to play the infinite game.
Book Synopsis Robust Control Theory in Hilbert Space by : Avraham Feintuch
Download or read book Robust Control Theory in Hilbert Space written by Avraham Feintuch and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 234 pages. Available in PDF, EPUB and Kindle. Book excerpt: An operator theoretic approach to robust control analysis for linear time-varying systems, with the emphasis on the conceptual similarity with the H control theory for time-invariant systems. It clarifies the major difficulties confronted in the time varying case and all the necessary operator theory is developed from first principles, making the book as self-contained as possible. After presenting the necessary results from the theories of Toeplitz operators and nest algebras, linear systems are defined as input-output operators and the relationship between stabilisation and the existence of co-prime factorisations is described. Uniform optimal control problems are formulated as model-matching problems and are reduced to four block problems, while robustness is considered both from the point of view of fractional representations and the "time varying gap" metric, as is the relationship between these types of uncertainties. The book closes with the solution of the orthogonal embedding problem for time-varying contractive systems. As such, this book is useful to both mathematicians and to control engineers.
Book Synopsis Generalized Homogeneity in Systems and Control by : Andrey Polyakov
Download or read book Generalized Homogeneity in Systems and Control written by Andrey Polyakov and published by Springer Nature. This book was released on 2020-02-05 with total page 454 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Control Methods in PDE-Dynamical Systems by : Fabio Ancona
Download or read book Control Methods in PDE-Dynamical Systems written by Fabio Ancona and published by American Mathematical Soc.. This book was released on 2007 with total page 416 pages. Available in PDF, EPUB and Kindle. Book excerpt: While rooted in controlled PDE systems, this 2005 AMS-IMS-SIAM Summer Research Conference sought to reach out to a rather distinct, yet scientifically related, research community in mathematics interested in PDE-based dynamical systems. Indeed, this community is also involved in the study of dynamical properties and asymptotic long-time behavior (in particular, stability) of PDE-mixed problems. It was the editors' conviction that the time had become ripe and the circumstances propitious for these two mathematical communities--that of PDE control and optimization theorists and that of dynamical specialists--to come together in order to share recent advances and breakthroughs in their respective disciplines. This conviction was further buttressed by recent discoveries that certain energy methods, initially devised for control-theoretic a-priori estimates, once combined with dynamical systems techniques, yield wholly new asymptotic results on well-established, nonlinear PDE systems, particularly hyperb These expectations are now particularly well reflected in the contributions to this volume, which involve nonlinear parabolic, as well as hyperbolic, equations and their attractors; aero-elasticity, elastic systems; Euler-Korteweg models; thin-film equations; Schrodinger equations; beam equations; etc. in addition, the static topics of Helmholtz and Morrey potentials are also prominently featured. A special component of the present volume focuses on hyperbolic conservation laws, to take advantage of recent theoretical advances with significant implications also on applied problems. in all these areas, the reader will find state-of-the-art accounts as stimulating starting points for further research.
Book Synopsis Control of Distributed Parameter and Stochastic Systems by : Shuping Chen
Download or read book Control of Distributed Parameter and Stochastic Systems written by Shuping Chen and published by Springer. This book was released on 2013-06-05 with total page 334 pages. Available in PDF, EPUB and Kindle. Book excerpt: In the mathematical treatment of many problems which arise in physics, economics, engineering, management, etc., the researcher frequently faces two major difficulties: infinite dimensionality and randomness of the evolution process. Infinite dimensionality occurs when the evolution in time of a process is accompanied by a space-like dependence; for example, spatial distribution of the temperature for a heat-conductor, spatial dependence of the time-varying displacement of a membrane subject to external forces, etc. Randomness is intrinsic to the mathematical formulation of many phenomena, such as fluctuation in the stock market, or noise in communication networks. Control theory of distributed parameter systems and stochastic systems focuses on physical phenomena which are governed by partial differential equations, delay-differential equations, integral differential equations, etc., and stochastic differential equations of various types. This has been a fertile field of research with over 40 years of history, which continues to be very active under the thrust of new emerging applications. Among the subjects covered are: Control of distributed parameter systems; Stochastic control; Applications in finance/insurance/manufacturing; Adapted control; Numerical approximation . It is essential reading for applied mathematicians, control theorists, economic/financial analysts and engineers.
Book Synopsis Infinite Dimensional Systems by : F. Kappel
Download or read book Infinite Dimensional Systems written by F. Kappel and published by . This book was released on 1984 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt:
