Work

On the Controllability of Nonlinear Systems with a Periodic Drift

Year: 2025

Type: article

Abstract: . This paper establishes sufficient conditions and necessary conditions for controllability of affine control systems. In contrast with previously known results, the convex hull of the control set contains the origin but is not assumed to be a neighborhood of the origin. Part of the results, in particular those on global controllability, are specific to systems where all solutions with zero control are periodic. The associated conditions are expressed by means of pushforwards along the flow of the drift, rather than in terms of Lie brackets. It turns out that they amount to local controllability of a time-varying linear approximation with constrained controls. Global and local results are given, as well as a few illustrative examples.

Source: SIAM Journal on Control and Optimization

DOI: 10.1137/22m1541381

Authors: J.-B. Caillau, L. Dell’Elce, A. Herasimenka, J.-B. Pomet

Institutions: Centre National de la Recherche Scientifique, Institut national de recherche en sciences et technologies du numérique, Université Côte d'Azur, Laboratoire Jean-Alexandre Dieudonné, University of Surrey

Language: English

Topic: Control and Stability of Dynamical Systems

Subfield: Control and Systems Engineering

Field: Engineering

Domain: Physical Sciences

Open Access status: green

OpenAlex ID: W4296396166

FWCI: 0.763

Cites: 22

Cited by: 2

Related to: 10