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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 foroptimality. 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.
List of contents
1 Mathematical Preliminaries.- 2 Linear Systems.- 3 Nonlinear Systems.- 4 Optimal Control: Existence Theory.- Optimal Control: Necessary Conditions of Optimality.- 6 Stochastic Systems Controlled by Vector Measures.- 7 Applications to Physical Examples.- Bibliography.- Index.
About the author
N.U. Ahmed is Emeritus Professor at the University of Ottawa. He has made significant contributions to functional analysis applied to systems and optimal control theory. Over his academic career, Dr. Ahmed has published 7 monographs and numerous journal articles in the general areas of systems and control theory, including partial differential equations, stochastic differential equations, abstract differential equations, integral equations and functional analysis. He received the University of Ottawa George Glinski award for excellence in research in 1989.
Shian Wang is a senior graduate student at the University of Ottawa. His research interests span the broad area of systems and control theory with extensive applications to intelligent transportation systems.
Report
"This book is a masterpiece of mathematical work where the authors joyfully stroll with the reader through the pleasant universe of control theory and its many applications. ... I think the authors did a very good job. Their contribution is surely going to be particularly helpful to applied mathematicians. It's a must read!" (Calvin Tadmon, SIAM Review, Vol. 64 (4), December, 2022)
