Noise-Induced Navigation in Non-convex Domains and Compact Manifolds
The paper constructs elementary feedback laws that achieve global asymptotic stability in a large sense for systems navigating connected Euclidean domains with obstacles and compact Riemannian manifolds. This is achieved by introducing controlled noise into the system dynamics, which helps bypass topological obstructions that prevent deterministic stabilization. The method extends to finding minimizers of strongly convex functions and addresses metastability in non-convex settings.