Dynamic Impulse Systems: Theory and Applications: 394 (Mathematics and Its Applications, 394) - Hardcover

Zavalishchin, S.T.; Sesekin, A.N.

Hardcover

ISBN 10: 0792343948 ISBN 13: 9780792343943

Publisher: Springer, 1997

Synopsis

A number of optimization problems of the mechanics of space flight and the motion of walking robots and manipulators, and of quantum physics, eco­ momics and biology, have an irregular structure: classical variational proce­ dures do not formally make it possible to find optimal controls that, as we explain, have an impulse character. This and other well-known facts lead to the necessity for constructing dynamical models using the concept of a gener­ alized function (Schwartz distribution). The problem ofthe systematization of such models is very important. In particular, the problem of the construction of the general form of linear and nonlinear operator equations in distributions is timely. Another problem is related to the proper determination of solutions of equations that have nonlinear operations over generalized functions in their description. It is well-known that "the value of a distribution at a point" has no meaning. As a result the problem to construct the concept of stability for generalized processes arises. Finally, optimization problems for dynamic systems in distributions need finding optimality conditions. This book contains results that we have obtained in the above-mentioned directions. The aim of the book is to provide for electrical and mechanical engineers or mathematicians working in applications, a general and systematic treat­ ment of dynamic systems based on up-to-date mathematical methods and to demonstrate the power of these methods in solving dynamics of systems and applied control problems.

About this title

Review

` ... is very well written and contains enough mathematical detail to permit the reader unfamiliar with the subject to quickly get up to speed in this important area of current research. Being unique in the field, the book is srongly recommended both for individual researchers in control systems and for the libraries.'
Applied Mechanics Reviews, 51:6 (1998)

Synopsis

This book provides a general and systematic treatment of dynamic systems. Based on up-to-date mathematical methods, including distribution theory, it demonstrates the power of these methods in solving dynamics of systems and applied control problems. First, new approaches to the construction problem of the general theory of linear dynamic systems are suggested. Then a new theory of differential equations with nonlinear operations over impulse input actions is developed. Finally, some singular optimization problems are treated on the subject of the mechanics of space flight, the motion transport manipulators in a viscous medium, quantum physics and economics. This volume will be of interest to electrical and mechanical engineers, as well as to applied mathematicians, whose work involves ordinary differential equations, control and optimization, circuit synthesis, or dynamics and vibration.

Edition details

• Publisher: Springer
• Publication date: 1997
• Language: English
• ISBN 10: 0792343948
• ISBN 13: 9780792343943
• Binding: Hardcover
• Number of pages: 271