Direct Methods in Control Problems
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Beschreibung
The primary focus of this book is on explicating the direct method approach. Historically, direct methods have not been fully exploited in control problems. The key is constructing convergent minimizing families. Integration methods (for example the gradient method) and representation methods (such as the Ritz-Galerkin and Finite Element methods) are examined in this text in an abstract (with concrete examples) functional analytic way. The aim is to consider direct methods from a unified general point of view and to provide a stimulus for future research. Explicitly, implicitly and by example, potential areas of research interest are indicated.
The book is a suitable reference for graduate students, researchers, applied mathematicians, and control engineers. Some of the material is of independent mathematical interest. The work may be used as a text for a graduate course or seminar on direct methods in control. A degree of mathematical sophistication and some knowledge of control theory is required.
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
Autor*in
Peter Falb
Themen in »Direct Methods in Control Problems«
Lévy processes deterministic systems direct methods finite element methods gradient method integration methods representation methods stochastic systems systems and control
Stimmen zu »Direct Methods in Control Problems«
“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)
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