Theory of Chattering Control with Applications to Astronautics, Robotics, Economics, and Engineering - How to Use Technology to Go Beyond Your Competition

Zelikin, Michail I.; Borisov, Vladimir F.

ISBN 10: 0817636188 / ISBN 13: 9780817636180

Verlag: Birkhäuser, 1994

Beschreibung

This is a Brand-new US Edition. This Item may be shipped from US or any other country as we have multiple locations worldwide.

Bestandsnummer des Verkäufers ABNR-92834

Bibliografische Details

• Titel: Theory of Chattering Control with Applications to Astronautics, Robotics, Economics, and Engineering - How to Use Technology to Go Beyond Your Competition
• Verlag: Birkhäuser
• Erscheinungsjahr: 1994
• Sprache: Englisch
• ISBN-10: 0817636188
• ISBN-13: 9780817636180
• Einband: Hardcover
• Zustand: New

Über diesen Titel

Inhaltsangabe

The common experience in solving control problems shows that optimal control as a function of time proves to be piecewise analytic, having a finite number of jumps (called switches) on any finite-time interval. Meanwhile there exists an old example proposed by A.T. Fuller [1961) in which optimal control has an infinite number of switches on a finite-time interval. This phenomenon is called chattering. It has become increasingly clear that chattering is widespread. This book is devoted to its exploration. Chattering obstructs the direct use of Pontryagin's maximum principle because of the lack of a nonzero-length interval with a continuous control function. That is why the common experience appears misleading. It is the hidden symmetry of Fuller's problem that allows the explicit solution. Namely, there exists a one-parameter group which respects the optimal trajectories of the problem. When published in 1961, Fuller's example incited curiosity, but it was considered only "interesting" and soon was forgotten. The second wave of attention to chattering was raised about 12 years later when several other examples with optimal chattering trajectories were 1 found. All these examples were two-dimensional with the one-parameter group of symmetries.

Críticas

"...a rich source of information."
― Mathematical Reviews

"This book is an excellent introduction to and survey of chattering optimal controls."
― SIAM Review

"The book is an interesting and modern study of some problems in control theory in the language of differential geometry."
― Zentralblatt Math