# Natural controlled invariant varieties for polynomial control problems

Date:
20.05.19
Times:
15:30
Place:
UAB - Dept. Matemàtiques (C1/-128)
Speaker:
Sebastian Walcher
University:
RWTH Aachen

Abstract

We consider polynomially nonlinear, input-affine control systems $\dot x= f(x)+g(x)u$ with a focus on invariant and controlled invariant algebraic varieties. Specifically we introduce and discuss natural controlled invariant varieties (NCIV) with respect to a given input matrix g, i.e. varieties which are controlled invariant sets of the control problem for any choice of the drift vector f. We use tools from commutative algebra and algebraic geometry in order to characterize NCIV's, provide some constructions and and present an algorithmic method to decide whether a variety is a NCIV with respect to an input matrix. The results and the algorithmic approach are illustrated by examples.