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Optimal Control Theory for Infinite Dimensional Systems

2012-12-06 Mathematics
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Release : 2012-12-06
Genre : Mathematics
Kind : eBook
Book Rating : 606/5 ( reviews)

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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. This book was released on 2012-12-06. 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.

Stochastic Optimal Control in Infinite Dimension

2017-06-22 Mathematics
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Release : 2017-06-22
Genre : Mathematics
Kind : eBook
Book Rating : 674/5 ( reviews)

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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. This book was released on 2017-06-22. 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.

Infinite Dimensional Optimization and Control Theory

1999-03-28 Computers
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Release : 1999-03-28
Genre : Computers
Kind : eBook
Book Rating : 253/5 ( reviews)

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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. This book was released on 1999-03-28. 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.

Representation and Control of Infinite Dimensional Systems

2007-04-05 Technology & Engineering
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Release : 2007-04-05
Genre : Technology & Engineering
Kind : eBook
Book Rating : 810/5 ( reviews)

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Book Synopsis Representation and Control of Infinite Dimensional Systems by : Alain Bensoussan

Download or read book Representation and Control of Infinite Dimensional Systems written by Alain Bensoussan. This book was released on 2007-04-05. Available in PDF, EPUB and Kindle. Book excerpt: This unified, revised second edition of a two-volume set is a self-contained account of quadratic cost optimal control for a large class of infinite-dimensional systems. The original editions received outstanding reviews, yet this new edition is more concise and self-contained. New material has been added to reflect the growth in the field over the past decade. There is a unique chapter on semigroup theory of linear operators that brings together advanced concepts and techniques which are usually treated independently. The material on delay systems and structural operators has not yet appeared anywhere in book form.

Control Theory of Infinite-Dimensional Systems

2020-06-25 Science
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Release : 2020-06-25
Genre : Science
Kind : eBook
Book Rating : 984/5 ( reviews)

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Book Synopsis Control Theory of Infinite-Dimensional Systems by : Joachim Kerner

Download or read book Control Theory of Infinite-Dimensional Systems written by Joachim Kerner. This book was released on 2020-06-25. Available in PDF, EPUB and Kindle. Book excerpt: This book presents novel results by participants of the conference “Control theory of infinite-dimensional systems” that took place in January 2018 at the FernUniversität in Hagen. Topics include well-posedness, controllability, optimal control problems as well as stability of linear and nonlinear systems, and are covered by world-leading experts in these areas. A distinguishing feature of the contributions in this volume is the particular combination of researchers from different fields in mathematics working in an interdisciplinary fashion on joint projects in mathematical system theory. More explicitly, the fields of partial differential equations, semigroup theory, mathematical physics, graph and network theory as well as numerical analysis are all well-represented.

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