Sliding mode control for a class of linear infinite-dimensional systems

Ismaïla Balogoun, Swann Marx, Franck Plestan

incompletemedium confidence

Category: math.DS
Journal tier: Specialist/Solid
Processed: Sep 28, 2025, 12:56 AM
arXiv Links: Abstract ↗PDF ↗

Audit review

The paper’s reduction, existence, and stability arguments for SMC and super–twisting essentially work and align with the model’s derivation, but a key hypothesis is missing: the controller divides by B*ϕ and thus requires B*ϕ ≠ 0. The paper claims this from Assumption 1(iii) by “setting t = T,” yet that quantifier manipulation does not follow from (2); approximate controllability only ensures there exists some t with B* T*(T−t)ϕ ≠ 0, not necessarily at t = T (so it does not imply B*ϕ ≠ 0) . The model also assumes B*ϕ ≠ 0 without properly justifying it. Aside from this gap (and the paper’s explicit restriction to the real case for super–twisting, which the model does not note ), the proofs are substantively consistent.

Referee report (LaTeX)

\textbf{Recommendation:} major revisions

\textbf{Journal Tier:} specialist/solid

\textbf{Justification:}

The paper offers a clean and useful framework to design SMC/STC for boundary-controlled PDEs by reducing to low-dimensional inclusions and reconstructing mild solutions via admissibility. However, a crucial structural requirement (B*ϕ ≠ 0 for the chosen eigenfunction of A\_L\^*) is missing or is incorrectly claimed from approximate controllability. This flaw affects the well-posedness of the control law. Clarifying/adding this hypothesis and tightening the mild/Filippov solution steps would make the contribution solid.