DyCon: Dynamic Control
The overall objective of the DyCon project is to make a breakthrough contribution in the broad area of Control of Partial Differential Equations (PDE) and their numerical approximation methods by addressing key unsolved issues appearing systematically in real life applications.
Partial Differential Equations (PDEs) are one of the main modelling ingredients in a diverse array of fields, from the management of natural resources, to meteorology, aeronautics, biomedicine or social behaviour, to name only a few. It constitutes a classical field in Mathematics in which significant progress has been done in the last decades. Despite of this, some of the key mathematical issues remain unsolved, particularly when addressing their dynamic control, aiming to understand how the dynamics of solutions can be driven to a desired target by means of external actuators or the tuning of some of the relevant parameters entering in the system. This wide class of open problems is amplified when addressing the challenging issue of developing the numerical techniques allowing to implement these control strategies computationally.
DyCon pursues three objectives: 1) to contribute with new key theoretical methods and results, 2) to develop the corresponding numerical tools, and 3) to build up new computational software, the DyCon-COMP computational platform, thereby bridging the gap to applications.
One of the problems that the DyCon project addresses from a mathematical perspective is the development of optimal control strategies in large temporal horizons, particularly important in those challenges that society faces in the medium and long term: energy, climate change, epidemiology, neurodegenerative diseases, waste management, wealth distribution, multiculturalism and immigration. The strength of the mathematical approach to these challenges, in symbiosis with Scientific Computing, lies on the fact that the main analytical and computational discoveries can then be implemented on a variety of models, addressing different applications.
DyCon also addresses relevant problems such as those related to: a) models involving memory effects, in which the dynamics is of an integro-differential nature, making the purely PDE approach insufficient; b) the need in practical applications to consider natural constraints and controls and states, which makes some of the ideal mathematical control strategies impossible to be implemented; and c) the interplay between discrete and continuous modelling, particularly important when addressing societal challenges. The global objective of DyCon is to answer to some of these key issues, but also to develop a computational platform allowing for a systematic numerical treatment of these problems.
