Stochastic Analysis, Control, Optimization and Applications: A Volume in Honor of W.H. Fleming (Systems & Control: Foundations & Applications)

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Presenting a thorough introductory exposition of optimal control theory, this work differs from the existing textbooks on the subject due to its emphasis on the economic interpretation of the mathematics and the qualitative properties of the solutions. Moreover, it is a modern exposition of optimal control theory in that it presents numerous complementary methods. It is aimed at first-year and second-year PhD students in economics, agricultural and resource economics, operations research, management science, and applied mathematics.

Optimal Control (Systems & Control: Foundations & Applications)

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Optimal Control (Systems & Control: Foundations & Applications)
Richard Vinter
Manufacturer: Birkhauser
ProductGroup: Book
Binding: Hardcover

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Partial Differential Equations (Graduate Studies in Mathematics, V. 19) GSM/19 (Graduate Studies in Mathematics)

ASIN: 0817640754

Book Description

Optimal control emerged as a distinct field of research only in recent decades. It provides a unified perspective of optimization problems, arising in scheduling and the control of engineering devices, that are beyond the reach of traditional analytical and computational techniques. In addition, the field has contributed significant advances to branches of applied mathematics and broad applications in process control, scheduling, robotics, resource economics, and other areas. Optimal Control brings together many of the important advances in 'nonsmooth' optimal control over the last two decades concerning necessary conditions, minimizer regularity and global optimality conditions associated with the Hamilton-Jacobi equation. The book's development and analysis is largely self-contained and incorporates numerous simplifications and unifying features for the subjects' key concepts and foundations. Features and Topics: * a comprehensive overview is provided for specialists and nonspecialists * authoritative, coherent and accessible coverage of the role of nonsmooth analysis in investigating minimizing curves for optimal control * chapter coverage of dynamic programming *explains the necessary conditions for nonconvex problems * chapter coverage of the regularity of minimizers This new book is an essential resource for an authoritative and comprehensive presentation of the foundations and application of nonsmooth optimal control. Postgraduates, researchers and professionals in systems, control, optimization and applied mathematics will find that the book is accessible, provides a rich source of insights and offers clear exposition.

H-Infinity Optimal Control and Related Minimax Design Problems: A Dynamic Game Approach (Systems & Control: Foundations & Applications)

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H-Infinity Optimal Control and Related Minimax Design Problems: A Dynamic Game Approach (Systems & Control: Foundations & Applications)
Tamer Basar , and Pierre Bernhard
Manufacturer: Birkhäuser Boston
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Binding: Hardcover

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ASIN: 0817638148

Book Description

One of the major concentrated activities of the past decade in control theory has been the development of the so-called 'H-infinity-optimal control theory', which addresses the issue of worst-case controller design for linear plants subject to unknown disturbances and plant uncertainties.

This second edition features a more streamlined presentation of the results included in the first edition and also contains substantial new material, reflecting new developments in the field since 1991. Among these are the nonlinear theory; connections between H-infinity-optimal control and risk sensitive stochastic control problems; H-infinity filtering for linear and nonlinear systems; and robustness considerations in the presence of regular and singular perturbations. Also included are a rather detailed description of the relationship between frequency-and time-domain approaches to robust controller design, and a complete set of results on the existence of value and characterization of optimal policies in finite- and infinite-horizon LQ differential games.

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H-infinity engineering continues to establish itself as a discipline of applied mathematics. As such, this extensively illustrated monograph makes a significant application of H-infinity theory to electronic amplifier design, demonstrating how recent developments in H-infinity engineering equip amplifier designers with new tools and avenues for research.

The amplification of a weak, noisy, wideband signal is a canonical problem in electrical engineering. Given an amplifier, matching circuits must be designed to maximize gain, minimize noise, and guarantee stability. These competing design objectives constitute a multiobjective optimization problem. Because the matching circuits are H-infinity functions, amplifier design is really a problem in H-infinity multiobjective optimization.

To foster this blend of mathematics and engineering, the author begins with a careful review of required circuit theory for the applied mathematician. Similarly, a review of necessary H-infinity theory is provided for the electrical engineer having some background in control theory. The presentation emphasizes how to (1) compute the best possible performance available from any matching circuits; (2) benchmark existing matching solutions; and (3) generalize results to multiple amplifiers.

As the monograph develops, many research directions are pointed out for both disciplines. The physical meaning of a mathematical problem is made explicit for the mathematician, while circuit problems are presented in the H-infinity framework for the engineer. A final chapter organizes these research topics into a collection of open problems ranging from electrical engineering, numerical implementations, and generalizations to H-infinity theory.

Customer Reviews:

chewy but good for you.......2006-04-27

I have not finished the book yet. But I appreciate the approach taken by Dr. Allen. Although written with the engineer in mind, the book right away associates the filter formalisms to the rich body of knowlege of analytic functions. It aims to connect the analytic character of real filters to the rich and mature theory. Don't fret! It's not an intro monologue. Rather, it's concise and comprehensive. For the mathematically inclined wishing to learn filter theory, this book is for you. Or for the math-savy engineer wishing to add electrical engineering depth, this book is also for you. But for the uninitiated and/or weak hearted, this book may benefit you.

Advances in Optimization and Approximation (Nonconvex Optimization and Its Applications)

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Advances in Optimization and Approximation (Nonconvex Optimization and Its Applications)

Manufacturer: Springer
ProductGroup: Book
Binding: Hardcover

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This book is a collection of research papers in optimization and approximation dedicated to Professor Minyi Yue of the Institute of Applied Mathematics, Beijing, China. The papers provide a broad spectrum of research on optimization problems, including scheduling, location, assignment, linear and nonlinear programming problems as well as problems in molecular biology. The emphasis of the book is on algorithmic aspects of research work in optimization. Special attention is paid to approximation algorithms, including heuristics for combinatorial approximation problems, approximation algorithms for global optimization problems, and applications of approximations in real problems. The work provides the state of the art for researchers in mathematical programming, operations research, theoretical computer science and applied mathematics.

Foundations of Bilevel Programming (Nonconvex Optimization and Its Applications)

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Foundations of Bilevel Programming (Nonconvex Optimization and Its Applications)
S. Dempe
Manufacturer: Springer
ProductGroup: Book
Binding: Hardcover

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ASIN: 1402006314

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Bilevel programming problems are hierarchical optimization problems where the constraints of one problem (the so-called upper level problem) are defined in part by a second parametric optimization problem (the lower level problem). If the lower level problem has a unique optimal solution for all parameter values, this problem is equivalent to a one-level optimization problem having an implicitly defined objective function. Special emphasize in the book is on problems having non-unique lower level optimal solutions, the optimistic (or weak) and the pessimistic (or strong) approaches are discussed. The book starts with the required results in parametric nonlinear optimization. This is followed by the main theoretical results including necessary and sufficient optimality conditions and solution algorithms for bilevel problems. Stationarity conditions can be applied to the lower level problem to transform the optimistic bilevel programming problem into a one-level problem. Properties of the resulting problem are highlighted and its relation to the bilevel problem is investigated. Stability properties, numerical complexity, and problems having additional integrality conditions on the variables are also discussed.
Audience: Applied mathematicians and economists working in optimization, operations research, and economic modelling. Students interested in optimization will also find this book useful.

Foundations of Generic Optimization, Volume 2: Applications of Fuzzy Control, Genetic Algorithms and Neural Networks (Mathematical Modelling: Theory and Applications)

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Foundations of Generic Optimization, Volume 2: Applications of Fuzzy Control, Genetic Algorithms and Neural Networks (Mathematical Modelling: Theory and Applications)

Manufacturer: Springer
ProductGroup: Book
Binding: Hardcover

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Book Description

This is a comprehensive overview of the basics of fuzzy control, which also brings together some recent research results in soft computing, in particular fuzzy logic using genetic algorithms and neural networks.

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Foundations of Generic Optimization: Volume 1: A Combinatorial Approach to Epistasis (Mathematical Modelling: Theory and Applications)

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Foundations of Generic Optimization: Volume 1: A Combinatorial Approach to Epistasis (Mathematical Modelling: Theory and Applications)
M. Iglesias , B. Naudts , and C. Vidal
Manufacturer: Springer
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Binding: Hardcover

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ASIN: 1402036663

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The success of a genetic algorithm when applied to an optimization problem depends upon several features present or absent in the problem to be solved, including the quality of the encoding of data, the geometric structure of the search space, deception or epistasis. This book deals essentially with the latter notion, presenting for the first time a complete state-of-the-art research on this notion, in a structured completely self-contained and methodical way.

In particular, it contains a refresher on the linear algebra used in the text as well as an elementary introductory chapter on genetic algorithms aimed at readers unacquainted with this notion.

In this way, the monograph aims to serve a broad audience consisting of graduate and advanced undergraduate students in mathematics and computer science, as well as researchers working in the domains of optimization, artificial intelligence, theoretical computer science, combinatorics and evolutionary algorithms.

Foundations of Mathematical Optimization: Convex Analysis without Linearity (Mathematics and Its Applications)

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Foundations of Mathematical Optimization: Convex Analysis without Linearity (Mathematics and Its Applications)
D. Pallaschke , and S. Rolewicz
Manufacturer: Springer
ProductGroup: Book
Binding: Hardcover

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ASIN: 0792344243

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Many books on optimization consider only finite dimensional spaces. This volume is unique in its emphasis: the first three chapters develop optimization in spaces without linear structure, and the analog of convex analysis is constructed for this case. Many new results have been proved specially for this publication. In the following chapters optimization in infinite topological and normed vector spaces is considered. The novelty consists in using the drop property for weak well-posedness of linear problems in Banach spaces and in a unified approach (by means of the Dolecki approximation) to necessary conditions of optimality. The method of reduction of constraints for sufficient conditions of optimality is presented. The book contains an introduction to non-differentiable and vector optimization.
Audience: This volume will be of interest to mathematicians, engineers, and economists working in mathematical optimization.

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