AN INPUT-TO-STATE SAFETY APPROACH TO ANOMALY-RESILIENT PARABOLIC PDES: APPLICATION TO CYBER-PHYSICAL BATTERY MODULES

The preprint formulates the PDE, boundary feedback, and safety/stability objectives clearly and derives a pISSf result via a barrier functional B(h) = ∫(h^2 + h_x^2) + h^2(m) − h_max^2 with conditions (22)–(25) and correctly proceeds to an ISS-type Lyapunov argument that yields V̇ ≤ −d3 V + d4||D||^2 + d5||u||^2 under additional conditions (39)–(41) (the d̃1–d̃3 positivity) . However, the ISSt criterion is stated with minus signs in front of the input terms (14), which is impossible to satisfy uniformly for arbitrary bounded inputs; the standard ISS form has plus signs. The same page also introduces a pISSf template with positively growing exponentials for the subtraction terms, which is nonstandard and weaker than what the analysis actually proves . The model identifies and corrects these issues, reproduces the d̃1–d̃3 coercivity conditions, and gives a standard ISS estimate with plus signs, using a clean energy method and standard 1-D trace/Poincaré tools. Minor gaps in the model’s writeup (explicit use of Poincaré to close V′ ≤ −λV) are standard to fill, whereas the paper’s ISSt definition/sign error requires revision.