Aram Arutyunov's Books

Optimal Impulsive Control

The Extension Approach

By: Aram Arutyunov,Dmitry Karamzin,Fernando Lobo Pereira

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Optimal Impulsive Control

The Extension Approach

By: Aram Arutyunov,Dmitry Karamzin,Fernando Lobo Pereira

Optimal Impulsive Control explores the class of impulsive dynamic optimization problems—problems that stem from the fact that many conventional optimal control problems do not have a solution in the classical setting—which is highly relevant with regard to engineering applications. The absence of a classical solution naturally invokes the so-called extension, or relaxation, of a problem, and leads to the notion of generalized solution which encompasses the notions of generalized control and trajectory; in this book several extensions of optimal control problems are considered within the framework of optimal impulsive control theory. In this framework, the feasible arcs are permitted to have jumps, while the conventional absolutely continuous trajectories may fail to exist. The authors draw together various types of their own results, centered on the necessary conditions of optimality in the form of Pontryagin’s maximum principle and the existence theorems, which shape a substantial body of optimal impulsive control theory. At the same time, they present optimal impulsive control theory in a unified framework, introducing the different paradigmatic problems in increasing order of complexity. The rationale underlying the book involves addressing extensions increasing in complexity from the simplest case provided by linear control systems and ending with the most general case of a totally nonlinear differential control system with state constraints. The mathematical models presented in Optimal Impulsive Control being encountered in various engineering applications, this book will be of interest to both academic researchers and practising engineers.

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Page Count

197

Publisher

Springer

Published Date

ISBN 10

3030022609

ISBN 13

9783030022600

Optimality Conditions: Abnormal and Degenerate Problems

By: Aram Arutyunov

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Optimality Conditions: Abnormal and Degenerate Problems

By: Aram Arutyunov

This book is devoted to one of the main questions of the theory of extremal problems, namely, to necessary and sufficient extremality conditions. The book consists of four parts. First, the abstract minimization problem with constraints is studied. The next chapter is devoted to one of the most important classes of extremal problems, the optimal control problem. Next, one of the main objects of the calculus of variations is studied, the integral quadratic form. Finally, local properties of smooth nonlinear mappings in a neighborhood of an abnormal point will be discussed. Audience: The book is intended for researchers interested in optimization problems. The book may also be useful for advanced students and postgraduate students.

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Page Count

318

Publisher

Springer Science & Business Media

Published Date

ISBN 10

0792366557

ISBN 13

9780792366553

Convex and Set-Valued Analysis

Selected Topics

By: Aram V. Arutyunov,Valeri Obukhovskii

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Convex and Set-Valued Analysis

Selected Topics

By: Aram V. Arutyunov,Valeri Obukhovskii

This textbook is devoted to a compressed and self-contained exposition of two important parts of contemporary mathematics: convex and set-valued analysis. In the first part, properties of convex sets, the theory of separation, convex functions and their differentiability, properties of convex cones in finite- and infinite-dimensional spaces are discussed. The second part covers some important parts of set-valued analysis. There the properties of the Hausdorff metric and various continuity concepts of set-valued maps are considered. The great attention is paid also to measurable set-valued functions, continuous, Lipschitz and some special types of selections, fixed point and coincidence theorems, covering set-valued maps, topological degree theory and differential inclusions. Contents: Preface Part I: Convex analysis Convex sets and their properties The convex hull of a set. The interior of convex sets The affine hull of sets. The relative interior of convex sets Separation theorems for convex sets Convex functions Closedness, boundedness, continuity, and Lipschitz property of convex functions Conjugate functions Support functions Differentiability of convex functions and the subdifferential Convex cones A little more about convex cones in infinite-dimensional spaces A problem of linear programming More about convex sets and convex hulls Part II: Set-valued analysis Introduction to the theory of topological and metric spaces The Hausdorff metric and the distance between sets Some fine properties of the Hausdorff metric Set-valued maps. Upper semicontinuous and lower semicontinuous set-valued maps A base of topology of the spaceHc(X) Measurable set-valued maps. Measurable selections and measurable choice theorems The superposition set-valued operator The Michael theorem and continuous selections. Lipschitz selections. Single-valued approximations Special selections of set-valued maps Differential inclusions Fixed points and coincidences of maps in metric spaces Stability of coincidence points and properties of covering maps Topological degree and fixed points of set-valued maps in Banach spaces Existence results for differential inclusions via the fixed point method Notation Bibliography Index

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Page Count

209

Publisher

Walter de Gruyter GmbH & Co KG

Published Date

ISBN 10

3110460300

ISBN 13

9783110460308

Optimal Impulsive Control

The Extension Approach

By: Aram Arutyunov,Dmitry Karamzin,Fernando Lobo Pereira

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Optimal Impulsive Control

The Extension Approach

By: Aram Arutyunov,Dmitry Karamzin,Fernando Lobo Pereira

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Solve jigsaw puzzle

Age

Page Count

197

Publisher

Springer

Published Date

ISBN 10

3030022609

ISBN 13

9783030022600

Convex and Set-Valued Analysis

Selected Topics

By: Aram V. Arutyunov,Valeri Obukhovskii

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Convex and Set-Valued Analysis

Selected Topics

By: Aram V. Arutyunov,Valeri Obukhovskii

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Page Count

244

Publisher

Walter de Gruyter GmbH & Co KG

Published Date

ISBN 10

3110460416

ISBN 13

9783110460414

Book's by Aram Arutyunov

Optimal Impulsive Control

Optimal Impulsive Control

Optimality Conditions: Abnormal and Degenerate Problems

Optimality Conditions: Abnormal and Degenerate Problems

Convex and Set-Valued Analysis

Convex and Set-Valued Analysis

Optimal Impulsive Control

Optimal Impulsive Control

Convex and Set-Valued Analysis

Convex and Set-Valued Analysis

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