Strong chain control sets and affine control systems

TL;DR

This paper introduces strong chain control sets for control-affine systems on non-compact manifolds, relating them to control flow transitivity, and analyzes their properties through embeddings into bilinear systems and topological conjugacy.

Contribution

It develops the concept of strong chain control sets for control-affine systems and links them to control flow transitivity, providing new insights into their controllability properties.

Findings

Strong chain control sets are related to strong chain transitivity of control flows.

Affine control systems on R^n are topologically conjugate to systems on the Poincaré sphere.

The paper analyzes chain controllability properties on spheres.

Abstract

For control-affine systems on non-compact manifolds, the notion of strong chain control sets is introduced and related to the strong chain transitivity of the associated control flows. Affine control systems on R^n are embedded into bilinear control systems in an extended state space and it is shown that they are topologically conjugate to the induced system on the northern hemisphere of the Poincar\'e sphere. This preserves strong chain control sets. Further chain controllability properties on spheres are analyzed