Franklin

Direct Methods in Control Problems / by Peter Falb.

Author/Creator:
Falb, Peter. author., Author,
Edition:
1st ed. 2019.
Publication:
New York, NY : Springer New York : Imprint: Birkhäuser, 2019.
Series:
Mathematics and Statistics (Springer-11649)
Format/Description:
Book
1 online resource (XIII, 311 pages) : 14 illustrations
Subjects:
System theory.
Automatic control.
Robotics.
Mechatronics.
Calculus of variations.
Approximation theory.
Probabilities.
Computer science -- Mathematics.
Local subjects:
Systems Theory, Control.
Control, Robotics, Mechatronics.
Calculus of Variations and Optimal Control; Optimization.
Approximations and Expansions.
Probability Theory and Stochastic Processes.
Computational Mathematics and Numerical Analysis.
System Details:
text file PDF
Summary:
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.
Contents:
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
Ritz-Galerkin Expansion
Karhunen-Loeve Expansion
Lévy Processes
Bibliography
Index .
Contributor:
SpringerLink (Online service)
Contained In:
Springer eBooks
Other format:
Printed edition:
Printed edition:
ISBN:
978-0-8176-4723-0
9780817647230
Publisher Number:
10.1007/978-0-8176-4723-0 doi
Access Restriction:
Restricted for use by site license.
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