Vector Measures and Control Systems
Author | : |
Publisher | : Elsevier |
Total Pages | : 191 |
Release | : 2011-09-21 |
Genre | : Mathematics |
ISBN | : 0080871313 |
Vector Measures and Control Systems
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Author | : |
Publisher | : Elsevier |
Total Pages | : 191 |
Release | : 2011-09-21 |
Genre | : Mathematics |
ISBN | : 0080871313 |
Vector Measures and Control Systems
Author | : N. U. Ahmed |
Publisher | : Springer Nature |
Total Pages | : 328 |
Release | : 2021-09-13 |
Genre | : Mathematics |
ISBN | : 3030821390 |
This book is devoted to the development of optimal control theory for finite dimensional systems governed by deterministic and stochastic differential equations driven by vector measures. The book deals with a broad class of controls, including regular controls (vector-valued measurable functions), relaxed controls (measure-valued functions) and controls determined by vector measures, where both fully and partially observed control problems are considered. In the past few decades, there have been remarkable advances in the field of systems and control theory thanks to the unprecedented interaction between mathematics and the physical and engineering sciences. Recently, optimal control theory for dynamic systems driven by vector measures has attracted increasing interest. This book presents this theory for dynamic systems governed by both ordinary and stochastic differential equations, including extensive results on the existence of optimal controls and necessary conditions for optimality. Computational algorithms are developed based on the optimality conditions, with numerical results presented to demonstrate the applicability of the theoretical results developed in the book. This book will be of interest to researchers in optimal control or applied functional analysis interested in applications of vector measures to control theory, stochastic systems driven by vector measures, and related topics. In particular, this self-contained account can be a starting point for further advances in the theory and applications of dynamic systems driven and controlled by vector measures.
Author | : Joseph Diestel |
Publisher | : American Mathematical Soc. |
Total Pages | : 338 |
Release | : 1977-06-01 |
Genre | : Mathematics |
ISBN | : 0821815156 |
In this survey the authors endeavor to give a comprehensive examination of the theory of measures having values in Banach spaces. The interplay between topological and geometric properties of Banach spaces and the properties of measures having values in Banach spaces is the unifying theme. The first chapter deals with countably additive vector measures finitely additive vector measures, the Orlicz-Pettis theorem and its relatives. Chapter II concentrates on measurable vector valued functions and the Bochner integral. Chapter III begins the study of the interplay among the Radon-Nikodym theorem for vector measures, operators on $L_1$ and topological properties of Banach spaces. A variety of applications is given in the next chapter. Chapter V deals with martingales of Bochner integrable functions and their relation to dentable subsets of Banach spaces. Chapter VI is devoted to a measure-theoretic study of weakly compact absolutely summing and nuclear operators on spaces of continuous functions. In Chapter VII a detailed study of the geometry of Banach spaces with the Radon-Nikodym property is given. The next chapter deals with the use of Radon-Nikodym theorems in the study of tensor products of Banach spaces. The last chapter concludes the survey with a discussion of the Liapounoff convexity theorem and other geometric properties of the range of a vector measure. Accompanying each chapter is an extensive survey of the literature and open problems.
Author | : Joergen Hoffmann-Joergensen |
Publisher | : Birkhäuser |
Total Pages | : 343 |
Release | : 2012-12-06 |
Genre | : Mathematics |
ISBN | : 3034880596 |
The title High Dimensional Probability is used to describe the many tributaries of research on Gaussian processes and probability in Banach spaces that started in the early 1970s. Many of the problems that motivated researchers at that time were solved. But the powerful new tools created for their solution turned out to be applicable to other important areas of probability. They led to significant advances in the study of empirical processes and other topics in theoretical statistics and to a new approach to the study of aspects of Lévy processes and Markov processes in general. The papers in this book reflect these broad categories. The volume thus will be a valuable resource for postgraduates and reseachers in probability theory and mathematical statistics.
Author | : D. Kölzow |
Publisher | : Springer |
Total Pages | : 342 |
Release | : 2006-11-14 |
Genre | : Mathematics |
ISBN | : 3540390693 |
Author | : Guillermo Curbera |
Publisher | : Springer Science & Business Media |
Total Pages | : 382 |
Release | : 2010-02-21 |
Genre | : Mathematics |
ISBN | : 3034602111 |
This volume contains a selection of articles on the theme "vector measures, integration and applications" together with some related topics. The articles consist of both survey style and original research papers, are written by experts in thearea and present a succinct account of recent and up-to-date knowledge. The topic is interdisciplinary by nature and involves areas such as measure and integration (scalar, vector and operator-valued), classical and harmonic analysis, operator theory, non-commutative integration, andfunctional analysis. The material is of interest to experts, young researchers and postgraduate students.
Author | : A. Bellow |
Publisher | : Springer |
Total Pages | : 423 |
Release | : 2006-11-14 |
Genre | : Mathematics |
ISBN | : 3540381074 |
Author | : J.M. Belley |
Publisher | : Springer |
Total Pages | : 335 |
Release | : 2006-12-08 |
Genre | : Mathematics |
ISBN | : 3540386904 |
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Author | : Og?uzto?reli |
Publisher | : Academic Press |
Total Pages | : 337 |
Release | : 1966-01-01 |
Genre | : Computers |
ISBN | : 0080955304 |
Time-Lag Control Systems
Author | : D. Kölzow |
Publisher | : Springer |
Total Pages | : 592 |
Release | : 2006-11-15 |
Genre | : Mathematics |
ISBN | : 3540392211 |