Per Dane's question: does LQR actually factor into the 2364x barrier
on n_high_trip, or is that just open-loop plant?
Answer: LQR IS included (A_cl = A - B*K), and the open-loop version is
catastrophically worse. Results on inv2_holds halfspaces:
open-loop LQR closed-loop
fuel_centerline 26.9M K bound 1137 K bound
t_avg_high_trip 788220 K bound 33.2 K bound
n_high_trip 27.4M x bound 1242 x bound
cold_leg_subcooled 1.8M K bound 77.8 K bound
gamma (level) 1.04e13 1.85e4
LQR improves every bound by ~20,000x — dramatic help — but the bounds
are still physically meaningless. The ceiling is set by plant anisotropy
(Lambda=1e-4 vs thermal timescales ~ seconds) forcing P to be
ill-conditioned regardless of LQR tuning. mu (slowest V-decay rate)
barely moves between OL and CL because both share the same slowest
thermal mode.
Clean motivation for the thesis chapter's move to polytopic / SOS
barriers: quadratic Lyapunov hits an anisotropy ceiling that no amount
of controller work can fix.
Co-Authored-By: Claude Opus 4.7 (1M context) <noreply@anthropic.com>
