Invariant submanifolds for affine control systems
Volume 124 / 2020
Annales Polonici Mathematici 124 (2020), 61-73
MSC: Primary 57R27, 58A17, 93B05; Secondary 37C10, 93C15.
DOI: 10.4064/ap190327-16-10
Published online: 11 December 2019
Abstract
Given an affine control system $\dot {\mathbf x} = f({\mathbf x}) + \sum _{j=1}^m g_j({\mathbf x}) u_j$ we present a method of construction of submanifolds that are invariant under controls assuming that the linear span of $f, g_1, \ldots , g_m$ has constant rank. We use the method of reduction of Pfaffian systems to the largest integrable subsystem and finding first integrals and generalized first integrals for the vector fields $f$ and $g_j$.
