Objective
This research project aims at the development of a radically new systematic approach to the field of set-valued numerical analysis. It is based on recent breakthrough results on the representation of sets as functions in a Banach space, and will allow the design of high performance numerical schemes for problems in dynamical systems and control theory, which cannot be solved efficiently within the traditional framework.
The last two decades have witnessed the successful development of grid-cell discretisations for the computation of characteristic sets of dynamical and control systems (attractors, reachable sets of control systems, etc.). The most popular software package based on this discretization is the computer program GAIO, which is used throughout the academic community and by institutions such as NASA.
Though grid-cell methods have reached a high degree of maturity, their computational complexity is very high, and they suffer massively from the curse of dimensionality. Since grid-cell discretisation possesses little structure, these schemes can at best be first-order convergent.
Therefore, this proposal aims at developing an alternative technique for the representation, analysis and numerical treatment of subsets of the Euclidean space. Instead of interpreting sets as collections of points without any further structure, sets will be grouped into set spaces that can be embedded into appropriate Banach spaces by means of a generalised support function. In this setting, sets can be handled by higher-order numerical methods such as Newton's scheme instead of first-order grid-cell methods.
The exploration of further properties of these set spaces, the development of efficient tools for the approximation of sets and the application to problems in dynamical systems and control theory will be an exciting, completely open field, and any additional insight will immediately open up new opportunities in set-valued numerical analysis and dynamics.
Fields of science (EuroSciVoc)
CORDIS classifies projects with EuroSciVoc, a multilingual taxonomy of fields of science, through a semi-automatic process based on NLP techniques. See: The European Science Vocabulary.
CORDIS classifies projects with EuroSciVoc, a multilingual taxonomy of fields of science, through a semi-automatic process based on NLP techniques. See: The European Science Vocabulary.
- natural sciences computer and information sciences software
- engineering and technology electrical engineering, electronic engineering, information engineering electronic engineering control systems
- natural sciences mathematics applied mathematics dynamical systems
- natural sciences mathematics applied mathematics numerical analysis
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Programme(s)
Multi-annual funding programmes that define the EU’s priorities for research and innovation.
Multi-annual funding programmes that define the EU’s priorities for research and innovation.
Topic(s)
Calls for proposals are divided into topics. A topic defines a specific subject or area for which applicants can submit proposals. The description of a topic comprises its specific scope and the expected impact of the funded project.
Calls for proposals are divided into topics. A topic defines a specific subject or area for which applicants can submit proposals. The description of a topic comprises its specific scope and the expected impact of the funded project.
Call for proposal
Procedure for inviting applicants to submit project proposals, with the aim of receiving EU funding.
Procedure for inviting applicants to submit project proposals, with the aim of receiving EU funding.
FP7-PEOPLE-2013-IEF
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Funding Scheme
Funding scheme (or “Type of Action”) inside a programme with common features. It specifies: the scope of what is funded; the reimbursement rate; specific evaluation criteria to qualify for funding; and the use of simplified forms of costs like lump sums.
Funding scheme (or “Type of Action”) inside a programme with common features. It specifies: the scope of what is funded; the reimbursement rate; specific evaluation criteria to qualify for funding; and the use of simplified forms of costs like lump sums.
Coordinator
SW7 2AZ London
United Kingdom
The total costs incurred by this organisation to participate in the project, including direct and indirect costs. This amount is a subset of the overall project budget.