We present a generalized Hadamard-Lévy type theorem concerning differentiable maps with singularities to verify their open mapping property, which provides a first theoretical justification to the homotopy continuation algorithm for the motion planning of non-linear control systems in the presence of singular controls, improving the strong bracket-generating condition in existing literatures to a weaker second-order condition, and derives a sufficient condition for local controllability.

BIOGRAPHY

Zhengping Ji is a postdoctoral researcher at Department of Mathematics, Friedrich-Alexander-Universität Erlangen-Nürnberg, Germany. He received the Ph.D. degree from Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing, China, in 2025. From 2023 to 2024, he was a Visiting Researcher with Laboratoire Jacques-Louis Lions, Sorbonne University, Paris, France. His research interests include nonlinear control systems, logical networks, and evolutionary games.