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Über dieses Buch

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.

Inhaltsverzeichnis

Frontmatter

Chapter 1. Mathematical Preliminaries

Abstract
This chapter presents most of the basic and important results from analysis required to read the book smoothly. It contains many relevant results from measure theory and abstract functional analysis used in the text.
N. U. Ahmed, Shian Wang

Chapter 2. Linear Systems

Abstract
This chapter is devoted to linear dynamic systems subject to forces determined by vector measures. It covers existence and uniqueness of solutions and regularity properties thereof.
N. U. Ahmed, Shian Wang

Chapter 3. Nonlinear Systems

Abstract
This chapter is devoted to nonlinear dynamic systems including differential inclusions subject to forces determined by vector measures. It covers existence and uniqueness of solutions and regularity properties thereof.
N. U. Ahmed, Shian Wang

Chapter 4. Optimal Control: Existence Theory

Abstract
This chapter deals with the question of existence of optimal controls from the class of 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.
N. U. Ahmed, Shian Wang

Chapter 5. Optimal Control: Necessary Conditions of Optimality

Abstract
This chapter presents necessary conditions of optimality for all the control problems considered in Chap. 4 and presents convergence theorems based on the necessary conditions of optimality.
N. U. Ahmed, Shian Wang

Chapter 6. Stochastic Systems Controlled by Vector Measures

Abstract
This chapter presents numerous results on existence of optimal controls and necessary conditions of optimality for systems governed by stochastic differential equations controlled by vector measures. Important convergence theorems are also presented guaranteeing convergence of any algorithm based on the necessary conditions of optimality.
N. U. Ahmed, Shian Wang

Chapter 7. Applications to Physical Examples

Abstract
This chapter presents computational algorithms applied to several practical examples. Detailed numerical results are presented which demonstrate the applicability of theoretical results developed in this book.
N. U. Ahmed, Shian Wang

Backmatter

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