A maximum principle for non-smooth optimal control problems with state contraints
Author: R. B. Vinter
Publisher:
Published: 1982
Total Pages: 26
ISBN-13:
DOWNLOAD EBOOKRead and Download eBook Full
Author: R. B. Vinter
Publisher:
Published: 1982
Total Pages: 26
ISBN-13:
DOWNLOAD EBOOKAuthor: Richard B. Vinter
Publisher:
Published: 1980
Total Pages: 26
ISBN-13:
DOWNLOAD EBOOKAuthor: Richard B. Vinter
Publisher:
Published: 1982
Total Pages: 21
ISBN-13:
DOWNLOAD EBOOKAuthor: Dan Tiba
Publisher: Springer
Published: 2006-11-14
Total Pages: 166
ISBN-13: 3540467556
DOWNLOAD EBOOKThe book is devoted to the study of distributed control problems governed by various nonsmooth state systems. The main questions investigated include: existence of optimal pairs, first order optimality conditions, state-constrained systems, approximation and discretization, bang-bang and regularity properties for optimal control. In order to give the reader a better overview of the domain, several sections deal with topics that do not enter directly into the announced subject: boundary control, delay differential equations. In a subject still actively developing, the methods can be more important than the results and these include: adapted penalization techniques, the singular control systems approach, the variational inequality method, the Ekeland variational principle. Some prerequisites relating to convex analysis, nonlinear operators and partial differential equations are collected in the first chapter or are supplied appropriately in the text. The monograph is intended for graduate students and for researchers interested in this area of mathematics.
Author: Aram Arutyunov
Publisher: Springer Science & Business Media
Published: 2000-10-31
Total Pages: 318
ISBN-13: 9780792366553
DOWNLOAD EBOOKThis book is devoted to one of the main questions of the theory of extremal problems, namely, to necessary and sufficient extremality conditions. The book consists of four parts. First, the abstract minimization problem with constraints is studied. The next chapter is devoted to one of the most important classes of extremal problems, the optimal control problem. Next, one of the main objects of the calculus of variations is studied, the integral quadratic form. Finally, local properties of smooth nonlinear mappings in a neighborhood of an abnormal point will be discussed. Audience: The book is intended for researchers interested in optimization problems. The book may also be useful for advanced students and postgraduate students.
Author: Fabio Ancona
Publisher: World Scientific
Published: 2008
Total Pages: 377
ISBN-13: 9812776060
DOWNLOAD EBOOKThe 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.
Author: Frank H. Clarke
Publisher: SIAM
Published: 1989-01-01
Total Pages: 94
ISBN-13: 0898712416
DOWNLOAD EBOOKPresents the elements of a unified approach to optimization based on 'nonsmooth analysis', a term introduced in the 1970's by the author, who is a pioneer in the field. Based on a series of lectures given at a conference at Emory University in 1986, this volume presents its subjects in a self-contained and accessible manner. The topics treated here have been in an active state of development. Focuses mainly on deterministic optimal control, the calculus of variations, and mathematical programming. In addition, it features a tutorial in nonsmooth analysis and geometry and demonstrates that the method of value function analysis via proximal normals is a powerful tool in the study of necessary conditions, sufficient conditions, controllability, and sensitivity analysis. The distinction between inductive and deductive methods, the use of Hamiltonians, the verification technique, and penalization are also emphasized.
Author: Philip Daniel Loewen
Publisher: American Mathematical Soc.
Published:
Total Pages: 172
ISBN-13: 9780821870198
DOWNLOAD EBOOKThis book provides a complete and unified treatment of deterministic problems of dynamic optimization, from the classical themes of the calculus of variations to the forefront of modern research in optimal control. At the heart of the presentation is nonsmooth analysis, a theory of local approximation developed over the last twenty years to provide useful first-order information about sets and functions lying beyond the reach of classical analysis. The book includes an intuitive and geometrically transparent approach to nonsmooth analysis, serving not only to introduce the basic ideas, but also to illuminate the calculations and derivations in the applied sections dealing with the calculus of variations and optimal control. Written in a lively, engaging style and stocked with numerous figures and practice problems, this book offers an ideal introduction to this vigorous field of current research. It is suitable as a graduate text for a one-semester course in optimal control or as a manual for self-study. Each chapter closes with a list of references to ease the reader's transition from active learner to contributing researcher. This series is published by the AMS for the Centre de Recherches Math\'ematiques.
Author: Francis H. Clarke
Publisher: Springer Science & Business Media
Published: 2008-01-10
Total Pages: 288
ISBN-13: 0387226257
DOWNLOAD EBOOKA 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.
Author: Marcio S. de Queiroz
Publisher: Springer Science & Business Media
Published: 2004-04-20
Total Pages: 380
ISBN-13: 9783540213307
DOWNLOAD EBOOKThis edited book contains selected papers presented at the Louisiana Conference on Mathematical Control Theory (MCT'03), which brought together over 35 prominent world experts in mathematical control theory and its applications. The book forms a well-integrated exploration of those areas of mathematical control theory in which nonsmooth analysis is having a major impact. These include necessary and sufficient conditions in optimal control, Lyapunov characterizations of stability, input-to-state stability, the construction of feedback mechanisms, viscosity solutions of Hamilton-Jacobi equations, invariance, approximation theory, impulsive systems, computational issues for nonlinear systems, and other topics of interest to mathematicians and control engineers. The book has a strong interdisciplinary component and was designed to facilitate the interaction between leading mathematical experts in nonsmooth analysis and engineers who are increasingly using nonsmooth analytic tools.