Singular Trajectories and their Role in Control Theory

ISBN-13: 9783540008385 / Angielski / Miękka / 2003 / 357 str.

Bernard Bonnard;Monique Chyba

Opis

Analyses the role of singular trajectories in control theory, containing about 60 exercises and problems. This book looks at the applications of singular trajectories to the optimisation of batch reactors. The theoretical part based on the Martinet case concerns the singularity analysis of singular trajectories in sub-Riemannian geometry.

Recenzje

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)

Spis treści

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