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Singular Trajectories and their Role in Control Theory de Bernard Bonnard

Singular Trajectories and their Role in Control Theory: Mathématiques et Applications, cartea 40

Autor Bernard Bonnard, Monique Chyba
en Limba Engleză Paperback – 12 mai 2003
The role of singular trajectories in control theory is analysed in this volume that contains about 60 exercieses and problems. A section is devoted to the applications of singular trajectories to the optimisation of batch reactors. The theoretical paart based on the Martinet case concerns the singulatrity analysis of singular trajectories in sub-Riemannian geometry. An algorithm is gibven to evaluate conjugate points and a final chapter discusses open problems. The volume will interest mathematicians and engineers.
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Specificații

ISBN-13: 9783540008385
ISBN-10: 3540008381
Pagini: 380
Ilustrații: XVI, 357 p.
Dimensiuni: 155 x 235 x 20 mm
Greutate: 0.53 kg
Ediția:2003
Editura: Springer Berlin, Heidelberg
Colecția Springer
Seria Mathématiques et Applications

Locul publicării:Berlin, Heidelberg, Germany

Public țintă

Research

Cuprins

Linear Systems and the Time Optimal Control Problem. - Exercises. - Optimal Control for Nonlinear Systems. - Exercises. - Geometric Optimal Control. - Exercises. - Singular Trajectories and Feedback Classification. - Exercises. - Controllability, Higher Order Maximum Principle, Legendre-Clebsch and Goh Necessary Optimality Conditions. - Exercises. - The Concept of Conjugate Points in the Time Minimal Control Problem for Singular Trajectories, C0-Optimality. - Time Minimal Control of Chemical Batch Reactors and Singular Trajectories. - Generic Properties of Singular Trajectories. - Exercises. - Singular Trajectories in Sub-Riemannian Geometry. - Exercises. - Micro-Local Resolution of the Singularity near a Singular Trajectory, Lagrangian Manifolds and Symplectic Stratifications. - Exercises. - Numerical Computations. - Conclusion and Perspectives. - Exercises. - References. - Index

Recenzii

From the reviews:
"This impressive book discusses the general theory of singular trajectories, and presents in detail a large number of important results … . The book is, however much broader and comprehensive than the title may suggest, and the authors have gone out of their way to make it accessible … . would be useful for a two-semester graduate course … . those who appreciate really deep mathematics, written with passion … will find this book rewarding and will read it … with enormous pleasure." (Héctor J. Sussmann, IEEE Transactions on Automatic Control, Vol. 50 (2), February, 2005)
"This book presents a detailed and comprehensive account of singular trajectories and their ramifications in control theory and related areas of mathematics. … it may be suitable as a textbook in an advanced course on nonlinear control theory. … Along the way the authors review a considerable amount of standard material from nonlinear control theory, thereby making the book accessible and useful to neophytes as well as experts." (Kevin A. Grasse, Mathematical Reviews, 2004 f)
"The book brings together a wealth of results on the topic of singular trajectories and its application, which for a large part was scattered up to now throughout the literature. Hence the book serves as a very valuable source of information for every researcher interested in these and related areas. Generally speaking, the book is well-accessible. … Summarizing, the book is a very welcome and useful addition to the literature, especially as a research monograph and source of information and inspiration." (A. J. Van der Schaft, Nieuw Archief voor Wiskunde, Vol. 8 (2), 2007)

Caracteristici

Includes supplementary material: sn.pub/extras