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 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.

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.

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.

Stochastic Evolution Systems

Stochastic Evolution Systems
Title Stochastic Evolution Systems PDF eBook
Author Boris L. Rozovsky
Publisher Springer
Pages 340
Release 2018-10-03
Genre Mathematics
ISBN 3319948938

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This monograph, now in a thoroughly revised second edition, develops the theory of stochastic calculus in Hilbert spaces and applies the results to the study of generalized solutions of stochastic parabolic equations. The emphasis lies on second-order stochastic parabolic equations and their connection to random dynamical systems. The authors further explore applications to the theory of optimal non-linear filtering, prediction, and smoothing of partially observed diffusion processes. The new edition now also includes a chapter on chaos expansion for linear stochastic evolution systems. This book will appeal to anyone working in disciplines that require tools from stochastic analysis and PDEs, including pure mathematics, financial mathematics, engineering and physics.

Forward-Backward Stochastic Differential Equations and their Applications

Forward-Backward Stochastic Differential Equations and their Applications
Title Forward-Backward Stochastic Differential Equations and their Applications PDF eBook
Author Jin Ma
Publisher Springer
Pages 285
Release 2007-04-24
Genre Mathematics
ISBN 3540488316

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This volume is a survey/monograph on the recently developed theory of forward-backward stochastic differential equations (FBSDEs). Basic techniques such as the method of optimal control, the 'Four Step Scheme', and the method of continuation are presented in full. Related topics such as backward stochastic PDEs and many applications of FBSDEs are also discussed in detail. The volume is suitable for readers with basic knowledge of stochastic differential equations, and some exposure to the stochastic control theory and PDEs. It can be used for researchers and/or senior graduate students in the areas of probability, control theory, mathematical finance, and other related fields.