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The study of nonlinear phenomena in aviation and aerospace includes developments in computer technology and the use of nonlinear mathematical models. Nonlinearities are a feature of aircraft dynamics and flight control systems and need to respond to achieve stability and performance. This multiauthor volume comprises selected papers from the confer
These Proceedings comprise the bulk of the papers presented at the Inter national Conference on Semigroups of Opemtors: Theory and Contro~ held 14-18 December 1998, Newport Beach, California, U.S.A. The intent of the Conference was to highlight recent advances in the the ory of Semigroups of Operators which provides the abstract framework for the time-domain solutions of time-invariant boundary-value/initial-value problems of partial differential equations. There is of course a firewall between the ab stract theory and the applications and one of the Conference aims was to bring together both in the hope that it may be of value to both communities. In these days when all scientific activity is judged by its value on "dot com" it is not surprising that mathematical analysis that holds no promise of an immediate commercial product-line, or even a software tool-box, is not high in research priority. We are particularly pleased therefore that the National Science Foundation provided generous financial support without which this Conference would have been impossible to organize. Our special thanks to Dr. Kishan Baheti, Program Manager.
These are the proceedings of the "AstroNet-II International Final Conference". This conference was one of the last milestones of the Marie-Curie Research Training Network on Astrodynamics "AstroNet-II", that has been funded by the European Commission under the Seventh Framework Programme. The aim of the conference, and thus this book, is to communicate work on astrodynamics problems to an international and specialised audience. The results are presented by both members of the network and invited specialists. The topics include: trajectory design and control, attitude control, structural flexibility of spacecraft and formation flying. The book addresses a readership across the traditional boundaries between mathematics, engineering and industry by offering an interdisciplinary and multisectorial overview of the field.
Trackability and Tracking of General Linear Systems deals with five classes of the systems, three of which are new, begins with the definition of time together with a brief description of its crucial properties and with the principles of the physical uniqueness and continuity of physical variables. They are essential for the natural tracking control synthesis. The book presents further new results on the new compact, simple and elegant calculus that enabled the generalization of the transfer function matrix concept and of the state concept, the completion of the trackability and tracking concepts together with the proofs of the trackability and tracking criteria, as well as the natural tracking control synthesis for all five classes of the systems. Features • Crucially broadens the state space concept and the complex domain fundamentals of the dynamical systems to the control systems. • Addresses the knowledge and ability necessary to study and design control systems that will satisfy the fundamental control goal. • Outlines new effective mathematical means for effective complete analysis and synthesis of the control systems. • Upgrades, completes and essentially generalizes the control theory beyond the existing boundaries. • Provides information necessary to create and teach advanced inherently upgraded control courses.
On becoming familiar with difference equations and their close re lation to differential equations, I was in hopes that the theory of difference equations could be brought completely abreast with that for ordinary differential equations. [HUGH L. TURRITTIN, My Mathematical Expectations, Springer Lecture Notes 312 (page 10), 1973] A major task of mathematics today is to harmonize the continuous and the discrete, to include them in one comprehensive mathematics, and to eliminate obscurity from both. [E. T. BELL, Men of Mathematics, Simon and Schuster, New York (page 13/14), 1937] The theory of time scales, which has recently received a lot of attention, was introduced by Stefan Hilger in his PhD thesis [159] in 1988 (supervised by Bernd Aulbach) in order to unify continuous and discrete analysis. This book is an intro duction to the study of dynamic equations on time scales. Many results concerning differential equations carryover quite easily to corresponding results for difference equations, while other results seem to be completely different in nature from their continuous counterparts. The study of dynamic equations on time scales reveals such discrepancies, and helps avoid proving results twice, once for differential equa tions and once for difference equations. The general idea is to prove a result for a dynamic equation where the domain of the unknown function is a so-called time scale, which is an arbitrary nonempty closed subset of the reals.
The primary purpose of control is to force desired behavior in an unpredictable environment, under the actions of unknown, possibly unmeasurable disturbances and unpredictable, and therefore probably nonzero, initial conditions. This means that tracking and tracking control synthesis are fundamental control issues. Surprisingly, however, tracking theory has not been well developed, and stability theory has dominated. Tracking Control of Linear Systems presents the fundamentals of tracking theory for control systems. The book introduces the full transfer function matrix F(s), which substantially changes the theory of linear dynamical and control systems and enables a novel synthesis of tracking control that works more effectively in real environments. An Introduction to the New Fundamentals of the Theory of Linear Control Systems The book begins by re-examining classic linear control systems theory. It then defines and determines the system full (complete) transfer function matrix F(s) for two classes of systems: input-output (IO) control systems and input-state-output (ISO) control systems. The book also discusses the fundamentals of tracking and trackability. It presents new Lyapunov tracking control algorithms and natural tracking control (NTC) algorithms, which ensure the quality of the tracking under arbitrary disturbances and initial conditions. This natural tracking control is robust, adaptable, and simple to implement. Advances in Linear Control Systems Theory: Tracking and Trackability This book familiarizes readers with novel, sophisticated approaches and methods for tracking control design in real conditions. Contributing to the advancement of linear control systems theory, this work opens new directions for research in time-invariant continuous-time linear control systems. It builds on previous works in the field, extending treatment o
This book aims to help the reader understand the linear continuous-time time-invariant dynamical systems theory and its importance for systems analysis and design of the systems operating in real conditions, i.e., in forced regimes under arbitrary initial conditions. The text completely covers IO, ISO and IIO systems. It introduces the concept of the system full matrix P(s) in the complex domain and establishes its link with the also newly introduced system full transfer function matrix F(s). The text establishes the full block diagram technique based on the use of F(s), which incorporates the Laplace transform of the input vector and the vector of all initial conditions. It explores the direct relationship between the system full transfer function matrix F(s) and the Lyapunov stability concept, definitions and conditions, as well as with the BI stability concept, definitions, and conditions. The goal of the book is to unify the study and applications of all three classes of the of the linear continuous-time time-invariant systems, for short systems.