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Nonsmooth Analysis And Control Theory

Author: Francis H. Clarke
Publisher: Springer Science & Business Media
ISBN: 0387226257
Size: 68.83 MB
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A clear and succinct presentation of the essentials of this subject, together with some of its applications and a generous helping of interesting exercises. Following an introductory chapter with a taste of what is to come, the next three chapters constitute a course in nonsmooth analysis and identify a coherent and comprehensive approach to the subject, leading to an efficient, natural, and powerful body of theory. The whole is rounded off with a self-contained introduction to the theory of control of ordinary differential equations. The authors have incorporated a number of new results which clarify the relationships between the different schools of thought in the subject, with the aim of making nonsmooth analysis accessible to a wider audience. End-of-chapter problems offer scope for deeper understanding.

Geometric Control And Nonsmooth Analysis

Author: Fabio Ancona
Publisher: World Scientific
ISBN: 9812776060
Size: 54.10 MB
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The aim of this volume is to provide a synthetic account of past research, to give an up-to-date guide to current intertwined developments of control theory and nonsmooth analysis, and also to point to future research directions.

Semiconcave Functions Hamilton Jacobi Equations And Optimal Control

Author: Piermarco Cannarsa
Publisher: Springer Science & Business Media
ISBN: 0817643362
Size: 15.12 MB
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First comprehensive and essentially self-contained exposition of the theory of semiconcave functions and their role in optimal control and Hamilton-Jacobi equations. Part I covers the general theory, summarizing and illustrating key results with significant examples. Part II is devoted to applications concerning the Bolza problem in the calculus of variations and optimal exit time problems for nonlinear control systems. Singularities are also studied for general semiconcave functions, then sharply estimated for solutions of Hamilton-Jacobi equations, and finally analyzed in connection with optimal trajectories of control systems. State-of-the-art reference for researchers in optimal control, the calculus of variations, and PDEs, as well as a good introduction for graduate students to modern dynamic programming for nonlinear control systems.

Functional Analysis Calculus Of Variations And Optimal Control

Author: Francis Clarke
Publisher: Springer Science & Business Media
ISBN: 1447148207
Size: 35.71 MB
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Functional analysis owes much of its early impetus to problems that arise in the calculus of variations. In turn, the methods developed there have been applied to optimal control, an area that also requires new tools, such as nonsmooth analysis. This self-contained textbook gives a complete course on all these topics. It is written by a leading specialist who is also a noted expositor. This book provides a thorough introduction to functional analysis and includes many novel elements as well as the standard topics. A short course on nonsmooth analysis and geometry completes the first half of the book whilst the second half concerns the calculus of variations and optimal control. The author provides a comprehensive course on these subjects, from their inception through to the present. A notable feature is the inclusion of recent, unifying developments on regularity, multiplier rules, and the Pontryagin maximum principle, which appear here for the first time in a textbook. Other major themes include existence and Hamilton-Jacobi methods. The many substantial examples, and the more than three hundred exercises, treat such topics as viscosity solutions, nonsmooth Lagrangians, the logarithmic Sobolev inequality, periodic trajectories, and systems theory. They also touch lightly upon several fields of application: mechanics, economics, resources, finance, control engineering. Functional Analysis, Calculus of Variations and Optimal Control is intended to support several different courses at the first-year or second-year graduate level, on functional analysis, on the calculus of variations and optimal control, or on some combination. For this reason, it has been organized with customization in mind. The text also has considerable value as a reference. Besides its advanced results in the calculus of variations and optimal control, its polished presentation of certain other topics (for example convex analysis, measurable selections, metric regularity, and nonsmooth analysis) will be appreciated by researchers in these and related fields.

Mathematics Of Complexity And Dynamical Systems

Author: Robert A. Meyers
Publisher: Springer Science & Business Media
ISBN: 1461418054
Size: 78.39 MB
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Mathematics of Complexity and Dynamical Systems is an authoritative reference to the basic tools and concepts of complexity, systems theory, and dynamical systems from the perspective of pure and applied mathematics. Complex systems are systems that comprise many interacting parts with the ability to generate a new quality of collective behavior through self-organization, e.g. the spontaneous formation of temporal, spatial or functional structures. These systems are often characterized by extreme sensitivity to initial conditions as well as emergent behavior that are not readily predictable or even completely deterministic. The more than 100 entries in this wide-ranging, single source work provide a comprehensive explication of the theory and applications of mathematical complexity, covering ergodic theory, fractals and multifractals, dynamical systems, perturbation theory, solitons, systems and control theory, and related topics. Mathematics of Complexity and Dynamical Systems is an essential reference for all those interested in mathematical complexity, from undergraduate and graduate students up through professional researchers.

Einf Hrung In Die Funktionalanalysis

Author: Reinhold Meise
Publisher: Springer-Verlag
ISBN: 3322803104
Size: 66.75 MB
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Dieses Buch wendet sich an Studenten der Mathematik und der Physik, welche über Grundkenntnisse in Analysis und linearer Algebra verfügen.