Singular Trajectories and their Role in Control Theory

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.

• 93B06, 93B27, 49K15
• feedback invariant
• optimal control
• singular extremals
• sub-Riemannian geometry
• symplectic geometry

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)

• LAAO, Université de Bourgogne Dépt. Mathématique, Dijon CX, France

  Bernard Bonnard

• University of Hawaii Dept. Mathematics, Honolulu, USA

  Monique Chyba

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