Alexander Kurzhanski - Böcker

This text gives an account of an ellipsoidal calculus and ellipsoidal techniques that allows presentation of the set-valued solutions to these problems in terms of approximating ellipsoidal-valued functions. Such an approach leads to effective computation schemes, an dopens the way to applications and implementations with computer animation, particularly in decision support systems. The problems treated here are those that involve calculation of attainability domains, of control synthesis under bounded controls, state constraints and unknown input disturbances, as well as those of "viability" and of the "bounding approach" to state estimation. The text ranges from a specially developed theory of exact set-valued solutions to the description of ellipsoidal calculus, related ellipsoidal-based methods and examples worked out with computer graphics. the calculus given here may also be interpreted as a generalized technique of the "interval analysis" type with an impact on scientific computation.

It is well known that the emphasis of mathematical modelling on the basis of available observations is first -to use the data to specify or refine the mathematical model, then - to analyze the model through available or new mathematical tools, and further on - to use this analysis in order to predict or prescribe (control) the future course of the modelled process. This is particularly done by specifying feedback control strategies (policies) that realize the desired goals. An important component of the overall process is to verify the model and its performance over the actual course of events. The given principles are also among the objectives of modern control theory, whether directed at traditional (aerospace, mechanics, regula­ tion, technology) or relatively new applications (environment, popula­ tion, finances and economics, biomedical issues, communication, and transport) . Among the specific features of the controlled processes in the mentioned areas are usually their dynamic nature and the uncertainty in their de­ scription.

These Proceedings report the scientific results of an International Workshop on Large-Scale Modelling and Interactive Decision Analysis organized Jointly by the System and Decision Sciences Program of the International Institute for Applied Systems Analysis (IIASA, located in Laxenburg, Austria), and the Institute for Informatics of the Academy of Sciences of the GDR (located in Berlin, GDR). The Workshop was held at a historically well-known place - the Wartburg Castl- near Eisenach (GDR). (Here Martin Luther translated the Bible into German.) More than fifty scientists representing thirteen countries participated. This Workshop is one of a series of meetings organizE!d by or In collaboration with IIASA about which two of the Lecture Notes In Economics and Mathematical Systems have already reported (Voi. 229 and Vol. 246). This time the aim of the meeting was to discuss methodological and practical problems associated with the modelling of large-scale systems and new approaches In interactive decision analysis based on advanced information processing systems.

It is already a tradition that conferences on operations research are organized by the Mathematisches Forschungsinstitut in Oberwolfach/Germany. The mean point of the 1987 conference was to discuss recentl.v developed methods in optimization theory derived from various fields of mathematics. On the other hand, the practical use of results in operations research is very important. In the last few years* essenti.al progress in this direction was made at the International Insti- tute for Applied Systems Analysis (IIASA) at Laxenburg/Austria. Therefore a three days workshop on Advanced Computation Techniques, Parallel Processing and Optimi- zation organized by IIASA and the University of Karlsruhe immediately followed the Oberwolfach Conference. This volume contains selected pape~s which have been presented at one of these conferences. It:is divided into five sections based on the above topics: I. Algorithms and Optimization Methods II. Optimization and Parallel Processing III. Graph Theory and Scheduling IV. Differential Equations and Operator Theory V. Applications. We would like to thank the director of the Mathematisches Forschungsinstitut Oberwolfach Prof. Dr. M.Barner and the International Institute for Applied Systems Analysis, particularly Prof. Dr. V. Kaftanov, and also to the director of the Computer Center of the University of Karlsruhe Prof. Dr. A. Schreiner for their support in organizing these conferences. We also appreciate the excellent coopera- tion of Springer Verlag. We also thank Dr. P. Recht, Dr. D. Solte and Dr. K. Wieder as well as*Mrs.