On Moment Theory and Controllability of One-Dimensional Vibrating Systems and Heating Processes

ISBN-13: 9783540551027 / Angielski / Miękka / 1992 / 177 str.

Werner Krabs

Opis

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).

Spis treści

Introduction: Finite-dimensional linear control systems and an outline of infinite-dimensional linear control problems.- Optimal damping of vibrations.- Optimal control of heating processes.