2411.19607
Lyapunov based dynamic controller designs for reach-and-avoid problems
Lukas Lanza, Philipp Braun
correctmedium confidence
- Category
- Not specified
- Journal tier
- Specialist/Solid
- Processed
- Sep 28, 2025, 12:56 AM
- arXiv Links
- Abstract ↗PDF ↗
Audit review
The paper’s Theorem 4.1 claims forward completeness, safety invariance, and convergence under bounded plant state, and provides a concise proof relying on previously established hybrid basic conditions and an ISS-Lyapunov argument. The candidate solution proves the same statements with a more constructive path-based analysis and explicit Lyapunov estimates for the virtual state. Minor technical gaps exist on both sides (e.g., continuity/boundedness of the tangential selection q̄i and some over-strong inequalities in the model’s Step 2), but these can be patched without changing the conclusions.
Referee report (LaTeX)
\textbf{Recommendation:} minor revisions
\textbf{Journal Tier:} specialist/solid
\textbf{Justification:}
The paper presents a coherent hybrid-Lyapunov approach to reach-and-avoid problems by combining a virtual obstacle-avoiding navigation field with a Lyapunov-based plant controller. The core theorem is correct and appropriately leverages classical hybrid-systems arguments and an ISS-Lyapunov estimate. Some steps are concise (e.g., forward completeness of the combined dynamics and the selection regularity of the tangential direction), and making these explicit would improve readability without altering the results.