Iman Mehrabinezhad

Carlos Argaez Garcia, október 30, 2019

Math colloquium

Fyrirlesari: Iman Mehrabinezhad, Háskóli Íslands

Titill: A new method for computation and verification of contraction metrics

Staðsetning: HB5 (Háskólabíó)
Tími: Föstudag 8.nóvember kl. 11:40


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).