Il giorno 26 settembre, alle ore 14:30, in aula 2107, il dottor Iman Mehrabi Nezhad (University of Iceland) terrà un seminario dal titolo
"Use of contraction metrics in approximating the basin of attraction for exponentially stable equilibria".
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Abstract: The determination of exponentially stable equilibria and their basin of attraction for a dynamical system given by a general autonomous ordinary differential equation can be achieved by means of a contraction metric. A contraction metric is a Riemannian metric with respect to which the distance between adjacent solutions decreases as time increases. The Riemannian metric can be expressed by a matrix-valued function on the phase space. The determination of a contraction metric can be achieved by approximately solving a matrix-valued partial differential equation by mesh-free collocation using Radial Basis Functions (RBF). Then, we combine the RBF method (to compute a contraction metric) with the CPA method to rigorously verify it. In particular, the computed contraction metric is interpolated by a continuous piecewise affine (CPA) metric at the vertices of a fixed triangulation, and by checking finitely many inequalities, we can verify that the interpolation is a contraction metric. Moreover, we show that, using sufficiently dense collocation points and a sufficiently fine triangulation, we always succeed with the construction and verification. This presentation is based on a joint work with Prof. Sigurdur Hafstein (University of Iceland), and Prof. Peter Giesl (University of Sussex, UK).