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Optimization and Finite Difference Approximations of Nonconvex Differential Inclusions with Free Time

1993
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Release : 1993
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Book Synopsis Optimization and Finite Difference Approximations of Nonconvex Differential Inclusions with Free Time by : University of Minnesota. Institute for Mathematics and Its Applications

Download or read book Optimization and Finite Difference Approximations of Nonconvex Differential Inclusions with Free Time written by University of Minnesota. Institute for Mathematics and Its Applications. This book was released on 1993. Available in PDF, EPUB and Kindle. Book excerpt:

Approximation and Optimization of Discrete and Differential Inclusions

2011-08-25 Mathematics
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Release : 2011-08-25
Genre : Mathematics
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Book Rating : 284/5 ( reviews)

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Book Synopsis Approximation and Optimization of Discrete and Differential Inclusions by : Elimhan N Mahmudov

Download or read book Approximation and Optimization of Discrete and Differential Inclusions written by Elimhan N Mahmudov. This book was released on 2011-08-25. Available in PDF, EPUB and Kindle. Book excerpt: 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

Introduction to the Theory of Differential Inclusions

2022-02-22 Mathematics
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Release : 2022-02-22
Genre : Mathematics
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Book Rating : 549/5 ( reviews)

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Book Synopsis Introduction to the Theory of Differential Inclusions by : Georgi V. Smirnov

Download or read book Introduction to the Theory of Differential Inclusions written by Georgi V. Smirnov. This book was released on 2022-02-22. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Nonsmooth Analysis and Geometric Methods in Deterministic Optimal Control

2012-12-06 Mathematics
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Release : 2012-12-06
Genre : Mathematics
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Book Rating : 893/5 ( reviews)

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Book Synopsis Nonsmooth Analysis and Geometric Methods in Deterministic Optimal Control by : Boris S. Mordukhovich

Download or read book Nonsmooth Analysis and Geometric Methods in Deterministic Optimal Control written by Boris S. Mordukhovich. This book was released on 2012-12-06. Available in PDF, EPUB and Kindle. Book excerpt: This IMA Volume in Mathematics and its Applications NONSMOOTH ANALYSIS AND GEOMETRIC METHODS IN DETERMINISTIC OPTIMAL CONTROL is based on the proceedings of a workshop that was an integral part of the 1992-93 IMA program on "Control Theory. " The purpose of this workshop was to concentrate on powerful mathematical techniques that have been de veloped in deterministic optimal control theory after the basic foundations of the theory (existence theorems, maximum principle, dynamic program ming, sufficiency theorems for sufficiently smooth fields of extremals) were laid out in the 1960s. These advanced techniques make it possible to derive much more detailed information about the structure of solutions than could be obtained in the past, and they support new algorithmic approaches to the calculation of such solutions. We thank Boris S. Mordukhovich and Hector J. Sussmann for organiz ing the workshop and editing the proceedings. We also take this oppor tunity to thank the National Science Foundation and the Army Research Office, whose financial support made the workshop possible. A vner Friedman Willard Miller, Jr. v PREFACE This volume contains the proceedings of the workshop on Nonsmooth Analysis and Geometric Methods in Deterministic Optimal Control held at the Institute for Mathematics and its Applications on February 8-17, 1993 during a special year devoted to Control Theory and its Applications. The workshop-whose organizing committee consisted of V. J urdjevic, B. S. Mordukhovich, R. T. Rockafellar, and H. J.

Variational Analysis and Generalized Differentiation I

2006-08-08 Mathematics
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Release : 2006-08-08
Genre : Mathematics
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Book Rating : 471/5 ( reviews)

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Book Synopsis Variational Analysis and Generalized Differentiation I by : Boris S. Mordukhovich

Download or read book Variational Analysis and Generalized Differentiation I written by Boris S. Mordukhovich. This book was released on 2006-08-08. Available in PDF, EPUB and Kindle. Book excerpt: Comprehensive and state-of-the art study of the basic concepts and principles of variational analysis and generalized differentiation in both finite-dimensional and infinite-dimensional spaces Presents numerous applications to problems in the optimization, equilibria, stability and sensitivity, control theory, economics, mechanics, etc.

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