Bücher der Reihe Mathematical Concepts and Methods in Science and Engineering

Linear stochastic systems are successfully used to provide mathematical models for real processes in fields such as aerospace engineering, communications, manufacturing, finance and economy. This monograph presents a useful methodology for the control of such stochastic systems with a focus on robust stabilization in the mean square, linear quadratic control, the disturbance attenuation problem, and robust stabilization with respect to dynamic and parametric uncertainty. Systems with both multiplicative white noise and Markovian jumping are covered.Key Features:-Covers the necessary pre-requisites from probability theory, stochastic processes, stochastic integrals and stochastic differential equations-Includes detailed treatment of the fundamental properties of stochastic systems subjected both to multiplicative white noise and to jump Markovian perturbations-Systematic presentation leads the reader in a natural way to the original results-New theoretical results accompanied by detailed numerical examples-Proposes new numerical algorithms to solve coupled matrix algebraic Riccati equations.The unique monograph is geared to researchers and graduate students in advanced control engineering, applied mathematics, mathematical systems theory and finance. It is also accessible to undergraduate students with a fundamental knowledge in the theory of stochastic systems.

Separation of the elements of classical mechanics into kinematics and dynamics is an uncommon tutorial approach, but the author uses it to advantage in this two-volume set. Students gain a mastery of kinematics first - a solid foundation for the later study of the free-body formulation of the dynamics problem.A key objective of these volumes, which present a vector treatment of the principles of mechanics, is to help the student gain confidence in transforming problems into appropriate mathematical language that may be manipulated to give useful physical conclusions or specific numerical results. In the first volume, the elements of vector calculus and the matrix algebra are reviewed in appendices. Unusual mathematical topics, such as singularity functions and some elements of tensor analysis, are introduced within the text. A logical and systematic building of well-known kinematic concepts, theorems, and formulas, illustrated by examples and problems, is presented offering insights into both fundamentals and applications. Problems amplify the material and pave the way for advanced study of topics in mechanical design analysis, advanced kinematics of mechanisms and analytical dynamics, mechanical vibrations and controls, and continuum mechanics of solids and fluids.Volume I of Principles of Engineering Mechanics provides the basis for a stimulating and rewarding one-term course for advanced undergraduate and first-year graduate students specializing in mechanics, engineering science, engineering physics, applied mathematics, materials science, and mechanical, aerospace, and civil engineering. Professionals working in related fields of applied mathematics will find it a practical review and a quick reference for questions involving basic kinematics.

In 1979, I edited Volume 18 in this series: Solution Methods for Integral Equations: Theory and Applications. Since that time, there has been an explosive growth in all aspects of the numerical solution of integral equations. By my estimate over 2000 papers on this subject have been published in the last decade, and more than 60 books on theory and applications have appeared. In particular, as can be seen in many of the chapters in this book, integral equation techniques are playing an increas- ingly important role in the solution of many scientific and engineering problems. For instance, the boundary element method discussed by Atkinson in Chapter 1 is becoming an equal partner with finite element and finite difference techniques for solving many types of partial differential equations. Obviously, in one volume it would be impossible to present a complete picture of what has taken place in this area during the past ten years. Consequently, we have chosen a number of subjects in which significant advances have been made that we feel have not been covered in depth in other books. For instance, ten years ago the theory of the numerical solution of Cauchy singular equations was in its infancy. Today, as shown by Golberg and Elliott in Chapters 5 and 6, the theory of polynomial approximations is essentially complete, although many details of practical implementation remain to be worked out.

Constrained Optimization and Image Space Analysis unites his results and presents optimization theory and variational inequalities in their light.It presents a new approach to the theory of constrained extremum problems, including Mathematical Programming, Calculus of Variations and Optimal Control Problems.

It is an incontestable fact that numerical analysis techniques are used rou tinely (although not always effectively) in virtually every quantitative field of scientific endeavor.

Multicriteria optimization has its roots in mathematical economics, in particular, in consumer economics as considered by Edgeworth and Pareto. Today, such an optimum is variously called "Pareto optimum" (after the Italian-French welfare economist who continued and expanded Edgeworth's work), "effi.

Separation of the elements of classical mechanics into kinematics and dynamics is an uncommon tutorial approach, but the author uses it to advantage in this two-volume set. Students gain a mastery of kinematics first ¿ a solid foundation for the later study of the free-body formulation of the dynamics problem.A key objective of these volumes, which present a vector treatment of the principles of mechanics, is to help the student gain confidence in transforming problems into appropriate mathematical language that may be manipulated to give useful physical conclusions or specific numerical results. In the first volume, the elements of vector calculus and the matrix algebra are reviewed in appendices. Unusual mathematical topics, such as singularity functions and some elements of tensor analysis, are introduced within the text. A logical and systematic building of well-known kinematic concepts, theorems, and formulas, illustrated by examples and problems, is presented offering insights into both fundamentals and applications. Problems amplify the material and pave the way for advanced study of topics in mechanical design analysis, advanced kinematics of mechanisms and analytical dynamics, mechanical vibrations and controls, and continuum mechanics of solids and fluids.Volume I of Principles of Engineering Mechanics provides the basis for a stimulating and rewarding one-term course for advanced undergraduate and first-year graduate students specializing in mechanics, engineering science, engineering physics, applied mathematics, materials science, and mechanical, aerospace, and civil engineering. Professionals working in related fields of applied mathematics will find it a practical review and a quick reference for questions involving basic kinematics.

This book is a self-contained text devoted to the numerical determination of optimal inputs for system identification. The book can be used for a two-semester course in control theory, system identification, and optimal inputs.

In the present monograph, Professor Gamkrelidze presents his current view of the fundamentals of optimal control theory. It contains, in essence, the principles of general control theory and proofs of the maximum principle and basic existence theorems of optimal control theory.

This book introduces two most important aspects of modern analysis: the theory of measure and integration and the theory of Banach and Hilbert spaces. It can serve as a text for a solid one-year course entitled "Measure and Integration Theory" or a com prehensive one-year course entitled "Banach Spaces, Hilbert Spaces, and Spectral Theory.

He derives many results that are of interest to practical structural engineers, such as optimum designs of structural elements submerged in a flowing fluid (which is of obvious interest in aircraft design, in ship building, in designing turbines, etc.).

This book is an outgrowth of formal graduate courses in multiple-criteria decision making (MCDM) that the author has taught at the University of Rochester, University of Texas at Austin, and University of Kansas since 1972.

This book deals with a very important problem in power system planning for countries in which hydrogeneration accounts for the greatest part of the system power production.

For many years it has been an article of faith of numerical analysts that the evaluation of derivatives of complicated functions should be avoided. The recent developments described in this text allow the evaluation of derivatives using simple automatic derivative evaluation subroutines pro grammed in FORTRAN or BASIC.

The reader who is not familiar with these subjects may refer to parts of Chapter 8 as needed or become somewhat familiar with them as prerequisite and treat Chapter 8 as Chapter O.

The author has found that a course taught three hours a week for a quarter can be based on the material in Chapters 1, 2, and 5 and the first three sections of Chapter 7.

Our purpose in writing this book is to provide a description of some of the applications of optimal control techniques to practical power system problems. It begins with an introductory chapter that briefly reviews the history of optimal control and its power system applications and also provides an outline of the text.

This book is intended to present an introductory treatment of the calculus of variations in Part I and of optimal control theory in Part II. Part II is devoted to the elementary aspects of the modern extension of the calculus of variations, the theory of optimal control of dynamical systems.

Proceedings of a Meeting held in Erice, Italy, September 3-10, 1991

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Functional analysis owes its OrIgms to the discovery of certain striking analogies between apparently distinct disciplines of mathematics such as analysis, algebra, and geometry.