# Numerical Analysis and Scientific Computing Seminar

## Polynomial approximations of the region of attraction of a polynomial control system

**Speaker:**
Didier Henrion, Toulouse

**Location:**
Warren Weaver Hall 1302

**Date:**
April 13, 2018, 10 a.m.

**Synopsis:**

We address the problem of computing the region of attraction (ROA) of a target set (e.g., a neighborhood of an equilibrium point) of a control system modeled by a ordinary differential equation with polynomial vector field and semi-algebraic constraints. We show that the ROA can be computed by solving an infinite-dimensional linear program over moments of occupation measures. In turn, this problem can be solved approximately with the Lasserre hierarchy of semidefinite programs. From the dual on polynomial sums of squares, we obtain a family of outer approximations converging in volume to the ROA when the degree of the polynomials tend to infinity.