On Moment Theory and Controllability of One-Dimensional Vibrating Systems and Heating Processes: 173 (Lecture Notes in Control and Information Sciences, 173) - Softcover

Krabs, Werner

Softcover

ISBN 10: 3540551026 ISBN 13: 9783540551027

Publisher: Springer, 1992

Synopsis

The main concern of this book is the application of infinite moment theory to the problem of controllability of one-di- mensional vibrating systems (like strings and beams) and heating processes. Distributed as well as boundary control is considered. In the case of vibrating systems trigonometric moment pro- blems are to be investigated which is done on the basis of an abstract moment theory in Hilbert spaces. Equivalently, alsothe theory of linear operator equations on Hilbert spa- ces ( partly with unbounded operators) is applied to the problem of controllability and time-minimal controllability. In the case of heating processes exponential moment problems are to be dealt with which is done on the basis of an ab- stract moment theory in Banach spaces. Time-minimal control- lability is also treated with the aid of the theory of line- aroperator equations on Banach spaces. Some advanced knowledge in functional analyis and on partial differential equations is preassumed for a fluent reader of the book, but parts of it are also readable with basic ma- thematical knowledge (for instance, the finite-dimensional part of the introduction).

About this title

Synopsis

The main concern of this book is the application of infinite moment theory to the problem of controllability of one-dimensional vibrating systems (like strings and beams) and heating processes. Distributed control and boundary control are considered. In the case of vibrating systems, trigonometric moment problems are investigated on the basis of abstract moment theory in Hilbert spaces. Additionally, the theory of linear operator equations on Hilbert spaces (partly with unbounded operators) is applied to the problem of controllability and time-minimal controllability. In the case of heating processes, exponential moment problems are dealt with on the basis of abstract moment theory in Banach spaces. Time-minimal controllability is also treated with the aid of the theory of linear operator equations on Banach spaces. Some advanced knowledge in functional analysis and on partial differential equations is required for a full reading of the book, but parts of it are also readable with basic mathematical knowledge.

Edition details

• Publisher: Springer
• Publication date: 1992
• Language: English
• ISBN 10: 3540551026
• ISBN 13: 9783540551027
• Binding: Paperback
• Edition number: 1
• Number of pages: 184