Dane Sabo 244a744e67 predicates: PJ-validity halfspace as an inv1_holds conjunct + reach tube plots ...

Following user's review feedback (point 1):

prompt_critical_margin_heatup: a new entry under safety_limits that
proves the PJ reduction's validity condition (beta - rho > 0 with
margin) rather than hand-waving it.  Controller-specific
specialization for heatup: under feedback linearization,
rho_total = Kp*(T_ref - T_c), so rho ≤ 0.5*beta iff T_c ≥ T_ref -
32.5.  Worst-case T_ref = T_c0 at ramp end, so T_c ≥ 275.85 is
sufficient, which our tight-entry reach clears trivially.

Conjoined into inv1_holds. Safety proofs now target BOTH the
physical bounds AND the conditions that make the PJ approximation
sound. Saves Dane's rigor-over-vibes instinct (saved to memory).

plot_reach_tubes.jl: four-panel visualization of a reach-result .mat:
  (1) T_c / T_hot / T_cold envelopes overlaid
  (2) ΔT_core = T_hot - T_cold (power proxy, right-axis MW)
  (3) rho envelope in dollars, with ±1$ prompt lines
  (4) n envelope
Operation-mode plot saved to docs/figures/reach_operation_tubes.png.
Heatup PJ version pending — needs full per-step data from the
running reach_heatup_pj_tight_full.jl.

reach_heatup_pj.jl + reach_heatup_pj_tight_full.jl now save
per-timestep envelopes (t_arr, Tc_lo_ts, Tc_hi_ts, ...) so the
plotting script can overlay tubes vs time.

Next up: polytopic / SOS barriers, Tikhonov error bound for PJ.

Co-Authored-By: Claude Opus 4.7 (1M context) <noreply@anthropic.com>

2026-04-21 16:28:02 -04:00

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