Mathematical Control Theory

Mathematical Control Theory
Title Mathematical Control Theory PDF eBook
Author Eduardo D. Sontag
Publisher Springer Science & Business Media
Pages 543
Release 2013-11-21
Genre Mathematics
ISBN 1461205778

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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.

Mathematical Control of Coupled PDEs

Mathematical Control of Coupled PDEs
Title Mathematical Control of Coupled PDEs PDF eBook
Author Irena Lasiecka
Publisher SIAM
Pages 248
Release 2002-01-01
Genre Mathematics
ISBN 0898714869

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

Mathematical Control Theory

Mathematical Control Theory
Title Mathematical Control Theory PDF eBook
Author Jerzy Zabczyk
Publisher Springer Science & Business Media
Pages 276
Release 2008
Genre Language Arts & Disciplines
ISBN 9780817647322

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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.

Mathematical Control Theory for Stochastic Partial Differential Equations

Mathematical Control Theory for Stochastic Partial Differential Equations
Title Mathematical Control Theory for Stochastic Partial Differential Equations PDF eBook
Author Qi Lü
Publisher Springer Nature
Pages 592
Release 2021-10-19
Genre Science
ISBN 3030823318

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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.

Stochastic Optimal Control in Infinite Dimension

Stochastic Optimal Control in Infinite Dimension
Title Stochastic Optimal Control in Infinite Dimension PDF eBook
Author Giorgio Fabbri
Publisher Springer
Pages 928
Release 2017-06-22
Genre Mathematics
ISBN 3319530674

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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.

Trends in Control Theory and Partial Differential Equations

Trends in Control Theory and Partial Differential Equations
Title Trends in Control Theory and Partial Differential Equations PDF eBook
Author Fatiha Alabau-Boussouira
Publisher Springer
Pages 285
Release 2019-07-04
Genre Mathematics
ISBN 3030179494

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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.

Optimal Control of Partial Differential Equations

Optimal Control of Partial Differential Equations
Title Optimal Control of Partial Differential Equations PDF eBook
Author Andrea Manzoni
Publisher Springer Nature
Pages 507
Release 2022-01-01
Genre Mathematics
ISBN 3030772268

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This is a book on optimal control problems (OCPs) for partial differential equations (PDEs) that evolved from a series of courses taught by the authors in the last few years at Politecnico di Milano, both at the undergraduate and graduate levels. The book covers the whole range spanning from the setup and the rigorous theoretical analysis of OCPs, the derivation of the system of optimality conditions, the proposition of suitable numerical methods, their formulation, their analysis, including their application to a broad set of problems of practical relevance. The first introductory chapter addresses a handful of representative OCPs and presents an overview of the associated mathematical issues. The rest of the book is organized into three parts: part I provides preliminary concepts of OCPs for algebraic and dynamical systems; part II addresses OCPs involving linear PDEs (mostly elliptic and parabolic type) and quadratic cost functions; part III deals with more general classes of OCPs that stand behind the advanced applications mentioned above. Starting from simple problems that allow a “hands-on” treatment, the reader is progressively led to a general framework suitable to face a broader class of problems. Moreover, the inclusion of many pseudocodes allows the reader to easily implement the algorithms illustrated throughout the text. The three parts of the book are suitable to readers with variable mathematical backgrounds, from advanced undergraduate to Ph.D. levels and beyond. We believe that applied mathematicians, computational scientists, and engineers may find this book useful for a constructive approach toward the solution of OCPs in the context of complex applications.