2007.08136
PURSUIT-EVASION GAME WITH HYBRID SYSTEM OF DYNAMICS
Mehdi Salimi
incompletehigh confidence
- Category
- Not specified
- Journal tier
- Note/Short/Other
- Processed
- Sep 28, 2025, 12:55 AM
- arXiv Links
- Abstract ↗PDF ↗
Audit review
The paper’s proof of Theorem 1.6 relies on two flawed steps: (i) an “equivalent” first-order reformulation that implicitly sets ė(0)=0 by writing e(0)=e0=e1ϕ+e0, collapsing the evader’s initial velocity and thereby making p(ϕ)=e(ϕ) hold only when e1=0 ; and (ii) an inadmissible Hölder/Cauchy–Schwarz step that bounds ∫0^ϕ(ϕ−t)^2∥ν(t)∥^2dt via (∫0^ϕ(ϕ−t)^4dt)^{1/2}(∫0^ϕ∥ν(t)∥^4dt)^{1/2} and then replaces the L4 term by the L2 budget Υ^2 to obtain the claimed √(ϕ^5/5) factor, which is not justified under only an L2 constraint . The model correctly identifies both issues, rigorously fixes the e1=0 case and gives the right φ^2Υ^2 bound, but its general-e1 “corrected phase set” does not fully control the additional cross term 2(e1, e(ϕ)−e0), so that part remains incomplete.
Referee report (LaTeX)
\textbf{Recommendation:} reject
\textbf{Journal Tier:} note/short/other
\textbf{Justification:}
The central theorem depends on (i) an inconsistent reduction that effectively removes the evader’s initial velocity, and (ii) an unjustified inequality replacing an L4 term by the L2 budget. These invalidate both the admissibility estimate and the claim p(ϕ)=e(ϕ) in general. While the idea can be corrected (e.g., for e1=0 with a φ\^2Υ\^2 bound, or by redesigning the phase constraint and strategy for general e1), the manuscript requires substantial corrections to statements and proofs.