EVENT DYNAMICS · Dynamics of non-expensive maps: Theory and Applications to discrete event systems
FP6 — Marie Curie Actions (Human Resources and Mobility)
- Duration
- 2006-01-01 → 2007-09-30
- EU contribution
- €129,850
- Participants
- 1
- Scheme
- EIF
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Results in brief
Final Activity Report Summary - EVENT DYNAMICS (Dynamics of Nonexpensive Maps: Theory and Applications to Discrete Event Systems)
Discrete event systems are a useful abstraction to analyse the performance of certain man-made systems including: digital circuits, communication networks, and manufacturing systems. In practice the designers of these systems are faced with a number of questions concerning the stability and long-term behaviour of such systems. In this project we have analysed various models that generalise the usual max-plus models for such systems. For a variety of models we have shown that such systems settle in a stable periodic regime. In addition, we have obtained results concerning the geometric structure of the set of stable steady states. Our work will assist designers of discrete event systems to select the properties of the system such that it will display the desired behaviour. In addition, it will help engineers to analyse the behaviour of discrete event systems. From a theoretical point of view much insight has been gained. In particular, we have further developed a non-linear version of the classical Perron-Frobenius theory. Perron-Frobenius theory was developed by Perron and Frobenius at the beginning of twentieth century and encompasses positive linear dynamical systems. The non-linear version of this theory provides the underlying framework for the study of the behaviour of discrete event systems. During the project the Marie-Curie fellow started, in collaboration with Roger Nussbaum, to write a research monograph on non-linear Perron-Frobenius theory, which will be published by Cambridge University Press.
Data: CORDIS, © European Union
Project objective
The objective of the research project is to investigate the dynamical behaviour of certain discrete event systems. Discrete event systems are a useful abstraction to analyse the performance of certain man-made systems including, digital circuits, communication networks, and manufacturing systems. In practice designers of these systems are faced with a number of dynamical questions: What is the long-term behaviour of the system? What are its stability properties? How fast does it operate? To answer these questions one needs to analyse a model.The main goal of the research project is to develop a theory for the dynamics of discrete event systems that can be modelled by so-called topical maps. Such a theory covers a variety of interesting systems and would be of practical value to engineers. In addition, it would advance the existing linear theory of max-plus systems to amore profound non-linear theory. The creation of such a theory is a mathematical challenge, as the standard dynamical systems techniques are not appropriate. To succeed, Dr Sparrow and I intend to develop novel techniques that are based on non-expansiveness properties of the system. We believe that, as a team, we could make considerable progress.In addition to expanding my research experience, the fellowship would give me the opportunity to work in the dynamics group at Warwick University. It would allow me to collaborate and interact with some of the world's leaders in dynamics. By attending postgraduate courses, weekly seminars, workshops, and symposia I would become acquainted with a variety of pure and applied topics in dynamical systems and enrich my knowledge of this field. The extensive visitors programme of the Mathematics Institute would allow me to meet many scientists and become part of a large international network of researchers in dynamics.
Original text from CORDIS.
Participants
- UNIVERSITY OF WARWICK · COVENTRYCoordinatorUnited Kingdom
Links
Data: CORDIS, © European Union