Scientific seminar on the differential and functional differential equation on topic "Boundary Value Problems for the Fractional Order Advection-Diffusion Equation" (chair: Professor A.L. Skubachevskii)
Sarychev Andrey Vasilievich, Department of Mathematics and Informatics U. Dini, University of Florence, Italy.
"Controllability on diffeomorphism groups and manifolds of smooth mappings".
The initial stimulus (jointly with A.A. Agrachev) of the work was the task of simultaneously controlling ensembles of dynamical systems or point ensembles and establishing controllability criteria. In the case of finite ensembles, the applicability and efficiency of the Lie methods of geometric control theory are obvious. In the case of infinite (continuum) ensembles, it is necessary to look for analogues of Lie methods for this infinite-dimensional controllability problem. The most general case is the problem of controllability on manifolds of smooth mappings (in the special case, on groups of diffeomorphisms), which is called ensemble controllability. In this paper, we formulate general controllability criteria and give examples of systems with the ensemble controllability property on some classical manifolds.