A generalized model of flocking with steering

The paper’s closed-loop flocking theorem (Theorem 2) derives the key differential inequality with an N^2 gain, d/dt dV ≤ −α N^2 ψ(dX) dV + dβ, and uses the Lyapunov functional E(dX,dV)=dV+α N^2∫_0^{dX}ψ to bound positions and drive dV→0 under dβ∈L^1 and dβ(t)→0; unconditional flocking follows if ∫_0^∞ψ=∞ . The candidate solution replaces N^2 by N in both the dissipation and Lyapunov weight, but still invokes the paper’s stronger threshold (with N^2), yielding a mismatch that breaks the Step 2 argument (one cannot deduce α N S(R) > dV(0)+∫ dβ from a bound involving α N^2 S_∞). The paper’s ψ construction, use of active sets, and convergence argument are sound , whereas the model’s proof hinges on the incorrect coefficient and a missing explicit justification of α>0 (the paper provides it via Lemma 4 under dβ∈L^1) .