Learning Dynamics Models with Stable Invariant Sets

The candidate’s Steps A–B closely match the paper’s construction and appendix proofs for invariance and Lyapunov/LaSalle-based convergence using V (5) and g (6), and the invariance enforcement (8) on the boundary is correctly leveraged (Proposition 1) . However, both the paper’s proof of Proposition 2 and the candidate’s argument implicitly require either α>0 or η>0 off S̃ to ensure strict decrease; the appendix proof asserts strict negativity without stating this design choice, which is incomplete for the α=0, η=0 case . More importantly, Corollary 1 maps back to x-space via f = φ^{-1} ∘ f̃ ∘ φ, but a correct coordinate change of vector fields requires the Jacobian pushforward (Dφ)^{-1}; mere bijectivity is insufficient. This flaw/incompleteness appears in both the paper and the candidate’s Step C .