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Unifying theories of learning and dynamical systems

Researchers have taken a deterministic dynamical systems approach towards the fundamental development of the analysis of control and random dynamical systems. Backed by EU funding, work in this area led to the development of a common framework allowing for systematic interaction of the theories of learning and dynamical systems.
Unifying theories of learning and dynamical systems
To support work on unifying the theories of learning and dynamical systems (both control and random), the 'Control, dynamics and stochastics' (CONDYS) project explored three directions in this field of research. The first covered the theory of set-valued dynamical systems as a unified framework to analyse control and random dynamical systems. The second focused on developing tools to analyse random dynamical systems, and the third on analysing and controlling systems with structure and symmetries.

Lying at the intersection of the theories of dynamical systems, probability and statistics, the research objective was to develop a mathematical, data-driven theory for dynamical systems. This could 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 development of such a theory has potential for major impact: it constitutes a novel point of departure from existing methodologies that rely on mathematical models.

CONDYS worked on the problem of model reduction of non-linear control systems using kernels methods. The project researchers used data to estimate the key quantities that appear in the study of control and random dynamical systems. Contacts were initiated in Europe and the United States, with talks given on project topics in both regions.

The progress made in CONDYS is likely to be put to advantage: common research projects at the intersection of control, random dynamical systems and statistical physics are being discussed.

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