A Power Tower Control: A New Sliding Mode Control

Malek GHANES, Jean-Pierre BARBOT

incompletelow confidence

Category: Not specified
Journal tier: Note/Short/Other
Processed: Sep 28, 2025, 12:56 AM
arXiv Links: Abstract ↗PDF ↗

Audit review

The paper’s central calculus lemma (the time derivative of ⌈a⌋|a|^α) is incorrect, and it underpins the entire backstepping construction and Lyapunov cancellations, so the main theorem is not established. The candidate model adopts the same erroneous identity and further proposes a power transform argument that cannot produce subunit exponents, so its claimed finite/fixed-time conclusions are also unsupported.

Referee report (LaTeX)

\textbf{Recommendation:} reject

\textbf{Journal Tier:} note/short/other

\textbf{Justification:}

The submission hinges on a new derivative identity for a “truncated power tower” function. That identity is obtained via a misuse of the chain rule (treating a product as an exponential of a product) and is therefore incorrect. Because the controller design and Lyapunov analysis depend critically on this identity, the core claims (including “guaranteed-finite time” convergence) are not established. The simulations are consistent with some stabilization behavior but cannot compensate for the analytical flaw. Substantial reworking—beginning with correct calculus and then appropriate finite/fixed-time arguments—would be needed. Given the central error and the breadth of revision required, rejection is appropriate.