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The proceedings of the Second US-Italy Seminar on Variable Structure Systems is published in this volume. Like the first seminar, its conception evolved from common research interests on bilinear systems at the Istituto di Automatica of Rome University and at the Electrical and Computer Engineering Department of Oregon State University. Again, the seminar was focused on variable structure systems in general. In this case, however, emphasis is given to applications in biology and economics along with theoretical investi gations which are so necessary to establish a unified theory and to motivate further developments in these applications of social significance. By bringing together the talents of social and biological scientists with those of engineers and mathematicians from throughout Italy and the United States, the seminar was intended to yield a cross-pollination of significant results and a base for more meaningful future research. The editors are encouraged by the progress, with which they hope the reader will agree, is made in this direction. No pretense is made, however, that completely satisfactory integration of theore tical results and applications has been accomplished at this time. Among the more important conclusions which have resulted from this seminar are that bilinear and more general variable structure models arise in a natural manner from basic principles for certain biological and economic processes.
The seminar for which the proceedings are published here evolved from a cooperative research program on bilinear systems and applications to immunology at the Oregon State University and at the University of Rome. The topics include more general forms of variable structure systems which may be divided into categories of mathematical system theory, economic applications and biological applications. Throughout the seminar there was emphasis on the integration of theory and app- cation. In most cases, theoretical derivations are motivated by their need to solve practical problems. In reading the proceedings, it becomes apparent that bilinear systems, quadratic systems and more general variable structure or adaptive systems become natural models in many cases and excellent approximations in others. It is seen that linear systems have very limited use particularly in economics and biology. Variable structure systems are analyzed in terms of structure,volterra kernels, system modelling, parameter identification,- controllability and Lie algebra to mention a few. Certainly, it ia nbt possible to present a complete tre- ment of these numerous topics, but at the Same time the unifying power of the systems approach and variable structure systems is shown.
This book is intended as a contribution to the theory of markets with imperfect information. The subject being nearly limitless, only certain selected topics are discussed. These are outlined in the Introduction (Ch. 0). The remainder of the book is divided into three parts. All results of economic significance are contained in Parts II & III. Part I introduces the main tools for the analysis, in particular the concept of an information structure. Although most of the material presented in Part I is not original, it is hoped that the detailed and self-contained exposition will help the reader to understand not only the following pages, but also the existing technical and variegated literature on markets with imperfect information. The mathematical prerequisites needed, but not explained in the text rarely go beyond elementary calculus and probability theory. Whenever more advanced concepts are used, I have made an effort to give an intuitive explanation as well, so that the argument can also be followed on a non-technical level (cf. e.g. the treatment of the "generic" viewpoint in Ch. 9). In the same spirit, discussion of mathematical assumptions is limited to those which have economic sig- ficance, whereas purely "technical" assumptions (like differentiability or integrability of certain functions) are usually made without comment whenever convenient. The logical interdependence of chapters is as follows: Ch. 3 . Ch. 1 /~I--=---- Ch. 4 Ch. 2 Ch. 8 ~I -=--- /"'-.... Ch.
First multi-year cumulation covers six years: 1965-70.
The mathematical theory of control became a ?eld of study half a century ago in attempts to clarify and organize some challenging practical problems and the methods used to solve them. It is known for the breadth of the mathematics it uses and its cross-disciplinary vigor. Its literature, which can befoundinSection93ofMathematicalReviews,wasatonetimedominatedby the theory of linear control systems, which mathematically are described by linear di?erential equations forced by additive control inputs. That theory led to well-regarded numerical and symbolic computational packages for control analysis and design. Nonlinear control problems are also important; in these either the - derlying dynamical system is nonlinear or the controls are applied in a n- additiveway.Thelastfourdecadeshaveseenthedevelopmentoftheoretical work on nonlinear control problems based on di?erential manifold theory, nonlinear analysis, and several other mathematical disciplines. Many of the problems that had been solved in linear control theory, plus others that are new and distinctly nonlinear, have been addressed; some resulting general de?nitions and theorems are adapted in this book to the bilinear case.
During the week of September 20-23, 1983, an International Workshop on Interactive Decision Analysis and Interpretative Computer Intelligence was held at the International Institute for Applied Systems Analysis (IIASA) in Laxenburg, Austria. More than fifty scientists representing seventeen coun tries participated. The aim of the Workshop was to review existing approaches to problems involving multiple conflicting objectives, to look at methods and techniques for interactive decision analysis, and to demonstrate theuse of existing interactive decision-support systems. The Workshop was motivated, firstly, by the realization that the rapid development of computers, especially microcomputers, will greatly increase the scope and capabilities of computerized decision-support systems. It is important to explore the potential of these systems for use in handling the complex technological, environmental, economic and social problems thatface the world today. Research in decision-support systems also has another, less tangible but possibly more important, motivation. The development of efficient sys tems for decision support requires a thorough understanding of the dif ferences between the decision-making processes in different nations and cultures. An understanding of the different rationales underlying decision making is not only necessary for the development of efficient decision support systems, but is also an important factor in encouraging inter national understanding and cooperation.
It is a great honor and privilege to have this opportunity of celebrating the 65th birthday of Professor Antonio Ruberti by holding an International Conference on Systems, Models and Feedback. The conference, and this volume which contains its proceedings, is a tribute to Professor Ruberti in acknowledgement of his major contributions to System Theory, at a time in which this area was emerging and consolidat ing as an independent discipline, his role as a leader of the Italian academic community, his activity in promoting and fostering close scientific relations between Italian and U.S. scholars in Systems and Control. The format of this conference is inspired by a series of seminars initi ated exactly twenty years ago under the direction of Professor Ruberti, in Italy, and Professor R. R. Mohler, in the U.S. By bringing together many authoritative talents from both countries, these seminars were instrumental in promoting the expansion of System Theory in new areas, notably that of Nonlinear Control, and were the key to successful scientific careers for many of the younger attendants.
The papers appearing in this Volume were selected from a collec tion of papers presented at the Internationa~ Symposium on Extrema~ Methods and Systems Ana~ysis on the Occasion of Professor A. Charnes' 60th Birthday, at the University of Texas in Austin, 13-15 September 1977. As coeditors, we have followed the normal editorial procedures of scholarly journals. We have obtained invaluable assistance from a number of colleagues who essentially performed the duties of associate editors, coordinating most of the reviews. All papers except those appearing in the Historica~ Perspectives section were refereed by at least two individuals with competency in the respective area. Because of the wide range and diversity of the topics, it would have been im possible for us to make a consistently rational selection of papers without the help of the associate editors and referees. We are indeed grateful to them. The breadth of extremal methods and systems analysis, suggested by the range of topics covered in these papers, is characteristic of the field and also of the scholarly work of Professor Charnes. Extre mal methods and systems analysis has been a pioneering and systematic approach to the development and application of new scientific theories and methods for problems of management and operations in both the pri vate and public sectors, spanning all major disciplines from economics to engineering.