Geometric theory of slow-fast systems to engineering and control problems

This research focuses on the applications of the geometric theory of slow-fast systems to engineering and control problems. A mathematical framework to study slow-fast systems is the Geometric Singular Perturbation Theory. GSPT studies, from a geometric point of view (i.e., with the language of invariant manifolds), dynamical systems having two or more distinct time scales. In this sense robots with flexible joints or networks satisfying certain conditions may be modeled as slow-fast systems. Many other examples of slow-fast systems can be found when studying chemical reactions, cell's biology, weather prediction, neural signals, etc. In this way, the theory of slow-fast systems can be used for model reduction or controller design purposes. Moreover, by using geometric tools we are able to get a better understanding and intuition of the dynamics of the systems. The goal of the project is to interconnect the ideas of GSPT and control theory to solve current, relevant, problems in engineering.