Invariant submanifolds for affine control systems

Abstract

Given an affine control system $\dot{\mathbf{x}}=f(\mathbf{x})+{\sum }_{j=1}^m{g}_j(\mathbf{x})u_j$ we present an algorithmic process of construction of submanifolds that are invariant under controls assuming that the linear span of $f,g_1,\dots ,g_m$ has constant rank. We use the method of reduction of Pfaffian systems to a largest integrable subsystem and finding the first integrals and the generalized first integrals for the vector fields.

11 pages