e69fd0a6f4
predicates.json is the single source of truth for concretizing the
FRET-spec predicates (t_avg_above_min, t_avg_in_range, p_above_crit,
inv1_holds, inv2_holds) as polytopes {x : A x <= b}. Until now these
were abstract booleans in the synthesis spec; reach analysis
re-invented ad-hoc thresholds that weren't tied to the spec. Closes
the Thrust-1-meets-Thrust-3 seam.
T_standby now defined as T_c0 - 60 F = 275 C (from user review).
Replaces the earlier simplification where shutdown IC held all temps
at T_cold0. 275 C is inside the model's +/-50 C trust region around
operating point and above coolant saturation at reduced pressure.
load_predicates.m in MATLAB reads the JSON and resolves rhs_expr
strings (which reference plant-derived constants like T_c0, T_cold0,
T_standby) into numeric bounds. Returns per-predicate (A_poly, b_poly)
plus a constants struct.
main_mode_sweep.m now pulls T_standby from predicates and uses it
for shutdown + heatup ICs. Heatup horizon extended to 90 min to
cover the wider 60 F -> operating range at 28 C/hr tech-spec limit.
reach_operation.m reads delta_safe_Tc from the t_avg_in_range
halfspace instead of hardcoding +/-5 K. Current concretization is
+/-2.78 C (~5 F); LQR reach still shows 28x margin.
inv1_holds and inv2_holds are marked PLACEHOLDER in the JSON —
engineering best guesses, not derived from a specific plant's tech
specs or a DNBR correlation. Revisit before thesis defense.
Hacker-Split: single-source concretization for FRET predicates,
end seam with reach.
Co-Authored-By: Claude Opus 4.7 (1M context) <noreply@anthropic.com>
Reachability
Continuous-mode verification for the PWR_HYBRID_3 hybrid controller.
Soundness status: APPROXIMATE
The current reach_operation.m result is not a sound reach tube for
the physical plant. It is a sound over-approximation of the
linearized closed-loop system (A_cl = A - BK around x_op) under
bounded disturbance. The linear model is itself an approximation of
the nonlinear plant (../plant-model/pke_th_rhs.m), and that
approximation error is not currently bounded or inflated into the tube.
Two paths to upgrade to a sound result:
- Nonlinear reach directly — CORA
nonlinearSys, JuliaReachBlackBoxContinuousSystem, or equivalent. More expensive but the honest answer. - Linear reach + Taylor-remainder inflation — compute an upper
bound on
||f_nl(x, u) - (A x + B u)||over the reach set (via Hessian norm estimate on each component off_nl) and inflate the linear tube by that bound. Less expensive, still rigorous.
Both are thesis-blocking for any safety claim. Deferred only until the per-mode plumbing is solid; it is not a "nice to have".
The current 5-orders-of-margin buffer (reach envelope ~0.03 K against a 5 K safety band) means linearization error would have to be huge to invalidate the conclusion, but that is vibes, not a proof.
Related open issues
- Saturation semantics.
ctrl_heatup.musessat(u, u_min, u_max). Saturation is formally a 3-mode piecewise-affine system. For heatup reach this has to be handled as (a) hybrid locations, or (b) proven dormant via reach onu_unsat. Not modeled in the current artifacts (operation-mode LQR saturation is dormant in practice but the proof is implicit). - Parametric uncertainty in α_f, α_c. Real plants have α drift
with burnup (~20%), boron (α_c ranges 10×), xenon. The
feedback-linearization in
ctrl_heatup.massumes exact α; a robust treatment would make α an interval and propagate parametric reach. Currently idealized — flag in the chapter.
What's here
Per-mode only. Following the compositionality argument in the thesis: verify each continuous mode separately, let the DRC handle discrete switching. Current focus: operation mode under LQR feedback.
What's here
linearization_at_op.mat— A, B, B_w and reference point, generated by../plant-model/test_linearize.m.reach_linear.m— box-zonotope propagation of the closed-loop linear model under bounded disturbance. Pure MATLAB, no external toolbox.barrier_lyapunov.m— Lyapunov-ellipsoid barrier certificate for the closed-loop linear system. Solves a Lyapunov equation, reports the smallest sub-level set containing the initial set and closed under the disturbance.reach_operation.m— end-to-end operation-mode reach: linearize at x_op, compute LQR gain, propagate zonotope reach set, check against thet_avg_in_rangepredicate.figures/— generated plots.
Running
From MATLAB:
cd reachability
reach_operation % computes reach set + plots
barrier_lyapunov % solves Lyapunov, reports invariant ellipsoid
Tool choice
Currently using a hand-rolled zonotope reach because:
- Avoids a ~0.5 GB CORA install for a first-pass result.
- Linear reach with bounded disturbance has a clean analytic form (matrix exponential on the state, integral of e^(A(t-s))·B_w·w ds for the disturbance).
- Stays inside MATLAB, which is where the plant model lives.
If we need nonlinear reach (and we will, for non-LQR controllers or larger reach sets where linearization error matters), the planned options are CORA (MATLAB) or JuliaReach (port the plant to Julia).
What this does NOT do yet
- Any sound reach tube (see top of this file).
- Nonlinear reach for the original P controller on operation.
- Heatup reach (ramped reference makes x* time-varying — needs trajectory-LQR or a different formulation, and the saturation semantics need to be made explicit).
- Shutdown, scram, initialization reach.
- Hybrid-system level verification (mode switching validity).
- Parametric robustness to α_f, α_c drift.