Noise-Induced Navigation in Non-convex Domains and Compact Manifolds

Key points

• Even if the system is fully actuated, topological obstructions generally prevent the existence of globally asymptotically stabilizing continuous feedback laws.1
• Using a criterion for asymptotic stability in the large that combines local Lyapunov stability with positive recurrence, we constructively show that one can construct elementary feedback laws that achieve global asymptotic stability in the large, of the target equilibrium point in connected Euclidean domains with obstacles and manifolds without boundary.1
• For Euclidean domains with obstacles, we also show that the method extends naturally to the problem of finding the minimizer of a strongly convex function with non-convex constraints.1
• Additionally, we study the role noise strength when there is a non-convex obstacle, in which case the system might show metastability.1

Sources (1)

• [1]Noise-Induced Navigation in Non-convex Domains and Compact Manifolds
  arXiv (AI, ML, NLP, CV, robotics, multi-agent) · Oct 7, 10:00 PM

  In this note, we study the problem of designing a feedback law that globally steers a system to a prescribed target configuration.

  Even if the system is fully actuated, topological obstructions generally prevent the existence of globally asymptotically stabilizing continuous feedback laws.

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