Direct Methods in Control Problems

Informed by the latest developments, this volume adds a much-needed focus on direct methodology to the literature on control and systems theory. New material presented includes representation techniques for stochastic systems involving Lévy processes.

Various general techniques have been developed for control and systems problems, many of which involve indirect methods. Because these indirect methods are not always effective, alternative approaches using direct methods are of particular interest and relevance given the advances of computing in recent years.

The focus of this book, unique in the literature, is on direct methods, which are concerned with finding actual solutions to problems in control and systems, often algorithmic in nature. Throughout the work, deterministic and stochastic problems are examined from a unified perspective and with considerable rigor. Emphasis is placed on the theoretical basis of the methods and their potential utility in a broad range of control and systems problems.

The book is an excellent reference for graduate students, researchers, applied mathematicians, and control engineers and may be used as a textbook for a graduate course or seminar ondirect methods in control.

Fills a gap in literature, covering direct methods applications in the control and systems context; takes into account recent significant advances in computing; most other books cover indirect methods New material is presented, in particular, a treatment of representation methods for stochastic systems involving Lévy processes Varied examples throughout are a valuable pedagogical tool and of independent interest to researchers and students For a broad audience of graduate students, researchers, applied mathematicians, and control engineers May be used as a textbook for a graduate course or seminar on direct methods in control

Autorentext

Peter Falb is Professor Emeritus of Applied Mathematics: Applied Mathematics at the Brown University in Providence, RI, USA. His research interests are in the areas of systems science and engineering, particularly algebraic and geometric methods, parametric dependence, numerical methods, multivariable linear systems, and infinite dimensional stochastic systems, as well as control and stability theory and mathematics of investment.

Zusammenfassung

"This is clearly a book aimed at specialists in control theory. It is more a monograph ... ." (Bill Satzer, MAA Reviews, November 28, 2021)

"This book offers a useful reading and provides interesting classroom material on the theory of finite-element indirect methods for optimal control problems." (Fernando Lobo Pereira, Mathematical Reviews, July, 2021)

"The book will become a valuable reference for researchers, engineers and students in the field of mathematics, management science, operations research, optimal control science and economics." (Savin Treanta, zbMATH 1444.93002, 2020)

Inhalt

Part I. Introduction.- Introductory Remarks.- Historical Perspective.- Outline of Contents.- Part II. Problem Statement.- Deterministic Systems.- Stochastic Systems.- General Problem.- Part III. The Direct Method Approach: Generalities.- General Approach.- Gradient and Integration Methods.- Representation Methods.- Part IV. Gradient and Integration Methods in Control Problems.- Computation of Gradients for ODE Problems.- Computation of Gradients for PDE Problems.- Integration Methods.- Part V. Representation Methods.- RitzGalerkin Expansion.- KarhunenLoeve Expansion.- Lévy Processes.- Bibliography.- Index