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Finite-difference Approximations and Optimal Control of Differential Inclusions

2015 Differential inclusions
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Release : 2015
Genre : Differential inclusions
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Book Synopsis Finite-difference Approximations and Optimal Control of Differential Inclusions by : Yuan Tian

Download or read book Finite-difference Approximations and Optimal Control of Differential Inclusions written by Yuan Tian. This book was released on 2015. Available in PDF, EPUB and Kindle. Book excerpt: This dissertation concerns the study of the generalized Bolza type problem for dynamic systems governed by constrained differential inclusions. We develop finite-discrete approximations of differential inclusions by using the implicit Euler scheme and the Runge-Kutta scheme for approximating time derivatives, while an appropriate well-posedness of such approximations is justified. Our principal result establishes the uniform approximation of strong local minimizers for the continuous-time Bolza problem by optimal solutions to the corresponding discretized finite-difference systems by the strengthen -norm approximation of this type in the case "intermediate" (between strong and weak minimizers) local minimizers under additional assumptions. Especially the implicitly discrete approximation is under the general ROSL setting. Finally, we derive necessary optimality conditions for each scheme for the discretized Bolza problems via suitable generalized differential constructions of variational analysis.

Approximation and Optimization of Discrete and Differential Inclusions

2011-08-25 Mathematics
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Release : 2011-08-25
Genre : Mathematics
Kind : eBook
Book Rating : 330/5 ( 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

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

1993
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Release : 1993
Genre :
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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
Download Approximation and Optimization of Discrete and Differential Inclusions PDF Online Free

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Release : 2011-08-25
Genre : Mathematics
Kind : eBook
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

Nonsmooth Analysis and Geometric Methods in Deterministic Optimal Control

2012-12-06 Mathematics
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Release : 2012-12-06
Genre : Mathematics
Kind : eBook
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.

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