Controllability on infinite-dimensional manifolds

TL;DR

This paper extends the Rashevsky-Chow theorem to control systems on infinite-dimensional manifolds modeled on convenient locally convex spaces, broadening the scope of controllability analysis beyond finite-dimensional settings.

Contribution

It generalizes the Rashevsky-Chow theorem to infinite-dimensional, convenient locally convex manifolds, providing a new framework for controllability in infinite-dimensional control systems.

Findings

Generalization of Rashevsky-Chow theorem to infinite-dimensional manifolds.

Framework applicable to non-normable locally convex spaces.

Enhances understanding of control system behavior in infinite-dimensional settings.

Abstract

Following the unified approach of A. Kriegl and P.W. Michor (1997) for a treatment of global analysis on a class of locally convex spaces known as convenient, we give a generalization of Rashevsky-Chow's theorem for control systems in regular connected manifolds modelled on convenient (infinite-dimensional) locally convex spaces which are not necessarily normable.