Final Report Summary - CONDYS (Control, dynamics and stochastics)
The fellowship has allowed B. Hamzi to work on unifying the theories of learning and (control and random) dynamical systems in the sense of developing a common framework where the theories of learning and dynamical systems interact in a systematic way. This research is at the intersection of the theories of dynamical systems, probability and statistics and its object is to develop a mathematical, data-driven theory for dynamical systems which can be used to analyse and predict random dynamical systems, as well as offer data-driven control strategies for non-linear systems on the basis of observed data (rather than a pre-described model). The impacts of such a theory are clear and constitute a novel point of departure from existing methodologies that rely on mathematical models.
Dr Hamzi worked on the problem of model reduction of non-linear control systems using kernels methods. He also worked on estimating from data key quantities that appear in the study of control and random dynamical systems (controllability and observability energies, invariant measure).
The objectives of the proposal were to:
1. transfer to Europe, the efforts that the applicant will make for the foundations and the application of the theory of set-valued dynamical systems;
2. transfer to Europe, the applicant's expertise in applying control-theoretic tools to random dynamical systems;
3. consolidate, in Europe, the research in the dynamical theory of control and the extension of tools from dynamical systems theory to control theory in view of controlling complex systems;
4. create discussions between mathematicians working in dynamical systems, control theoreticians and control engineers;
5. attract potential beneficiaries from both academic and industry increasing financial contributions to the field;
6. motivate control engineers to learn more about dynamical systems theory and system dynamicists to learn more about control theory;
7. maintain close relationships with different teams on control theory and dynamical systems within Europe;
8. publish results in refereed academic journals and communicating them at major international conferences;
9. give regular seminars in different universities in the United Kingdom and Europe by introducing control theory and its problems to the experts in dynamical systems theory and also introducing the different techniques that dynamical systems theory has to offer to control theory to control engineers.
B. Hamzi gave different talks in Europe and the United States (US). He initiated many contacts in Europe and the US. For instance, he has an ongoing collaboration with Prof. M. Pontil from UCL and Dr Opmeer from Bath University. He was invited by Prof. O. Bandtlow (Queen Mary University) with whom he started discussions about common research projects at the intersection of control, random dynamical systems and statistical physics. He also initiated contacts with Prof. E. Wit, Dr J. Gonzalez (University of Groningen). Prof. F. Bach (ENS, Paris), Prof. F. d'Alche-Buc (Universite d'Evry, Paris).
In the US, he initiated a collaboration with Prof. E. Abed (UMD, College Park). He was invited to give a talk by Prof. Dolgopyat, a leading expert in ergodic theory, where he also got chance to discuss with Prof. M. Freidlin, a leading expert in random dynamical systems, and Prof. S. Cerrai. He continued his collaboration with J. Bouvrie (MIT) and got chance to visit him at MIT and to get introduced to L. Rosasco (MIT). He was also invited by Prof. F. Colonius to give a talk and for a research visit at the University of Augsburg (Germany).
Dr Hamzi worked on the problem of model reduction of non-linear control systems using kernels methods. He also worked on estimating from data key quantities that appear in the study of control and random dynamical systems (controllability and observability energies, invariant measure).
The objectives of the proposal were to:
1. transfer to Europe, the efforts that the applicant will make for the foundations and the application of the theory of set-valued dynamical systems;
2. transfer to Europe, the applicant's expertise in applying control-theoretic tools to random dynamical systems;
3. consolidate, in Europe, the research in the dynamical theory of control and the extension of tools from dynamical systems theory to control theory in view of controlling complex systems;
4. create discussions between mathematicians working in dynamical systems, control theoreticians and control engineers;
5. attract potential beneficiaries from both academic and industry increasing financial contributions to the field;
6. motivate control engineers to learn more about dynamical systems theory and system dynamicists to learn more about control theory;
7. maintain close relationships with different teams on control theory and dynamical systems within Europe;
8. publish results in refereed academic journals and communicating them at major international conferences;
9. give regular seminars in different universities in the United Kingdom and Europe by introducing control theory and its problems to the experts in dynamical systems theory and also introducing the different techniques that dynamical systems theory has to offer to control theory to control engineers.
B. Hamzi gave different talks in Europe and the United States (US). He initiated many contacts in Europe and the US. For instance, he has an ongoing collaboration with Prof. M. Pontil from UCL and Dr Opmeer from Bath University. He was invited by Prof. O. Bandtlow (Queen Mary University) with whom he started discussions about common research projects at the intersection of control, random dynamical systems and statistical physics. He also initiated contacts with Prof. E. Wit, Dr J. Gonzalez (University of Groningen). Prof. F. Bach (ENS, Paris), Prof. F. d'Alche-Buc (Universite d'Evry, Paris).
In the US, he initiated a collaboration with Prof. E. Abed (UMD, College Park). He was invited to give a talk by Prof. Dolgopyat, a leading expert in ergodic theory, where he also got chance to discuss with Prof. M. Freidlin, a leading expert in random dynamical systems, and Prof. S. Cerrai. He continued his collaboration with J. Bouvrie (MIT) and got chance to visit him at MIT and to get introduced to L. Rosasco (MIT). He was also invited by Prof. F. Colonius to give a talk and for a research visit at the University of Augsburg (Germany).