1eab154847
Polytopic (Nagumo face-by-face LP check) and SOS polynomial
(Prajna-Jadbabaie w/ CSDP) barrier attempts on operation mode.
**Polytopic (barrier_polytopic.jl):** the naive check on
inv2_holds ∩ precursor_tube_bounds fails — 16 of 18 faces can be
crossed under A_cl. This is EXPECTED: safety halfspaces alone form
a set too big for LQR to contract from everywhere. The correct
approach is Blanchini's pre-image iteration (max robustly controllable
invariant set). Sketched in the script; 2-3 days to implement properly.
**SOS (barrier_sos_2d.jl):** a working proof of concept.
CSDP returns OPTIMAL on a 2-state projection of the operation mode
(dn, dT_c) with:
X_entry = |dn| ≤ 0.01, |dT_c| ≤ 0.1
X_unsafe = dn ≥ 0.15 (high-flux-trip direction)
Dynamics = reduced 2×2 A_cl after LQR.
No disturbance (B_w projects to 0 in this subset).
Global decrease condition (-(∇B·f) SOS) instead of Putinar ∂{B=0}.
Result: a degree-4 polynomial B(x) satisfying all three barrier
conditions. Coefficients printed. First non-quadratic barrier
artifact for this plant.
Caveats:
- 2D projection loses precursor coupling.
- Disturbance ignored in this projection.
- Global-decrease is stronger than the Putinar ∂{B=0} condition;
the latter requires bilinear σ_b·B formulation (BMI) and
iterative solvers. Deferred.
- Scaling to 10-state degree-4 gives SDP ~ 1000×1000; CSDP may
choke. Mosek or MOSEK-free SDP (SCS) might handle.
JuMP, HiGHS, SumOfSquares, DynamicPolynomials, CSDP all added to
Project.toml.
Co-Authored-By: Claude Opus 4.7 (1M context) <noreply@anthropic.com>
code
Plant model, controllers, and reach-analysis toolchain for the HAHACS preliminary example. All Julia.
What this is
A 10-state coupled neutronics + thermal-hydraulics model (point kinetic equations + lumped thermal loop) with continuous-mode controllers for each of the DRC modes (shutdown, heatup, operation, scram), plus a hand-rolled linear reach-tube propagator, a Lyapunov-ellipsoid barrier attempt, and scaffolding for TMJets-based nonlinear reach.
Ported from MATLAB on 2026-04-20 once the reach experiments made it
clear that Julia's stack (OrdinaryDiffEq, MatrixEquations,
ReachabilityAnalysis, LazySets, @taylorize) was the right tool
for everything we need going forward. The MATLAB originals are in
the git history.
Running
First time:
cd code
julia --project=. -e 'using Pkg; Pkg.instantiate()'
Subsequent:
julia --project=. scripts/main_mode_sweep.jl # all 5 DRC modes, figures
julia --project=. scripts/reach_operation.jl # operation-mode linear reach
julia --project=. scripts/barrier_lyapunov.jl # Lyapunov barrier attempt
julia --project=. scripts/barrier_compare_OL_CL.jl # OL vs CL barrier
julia --project=. scripts/reach_heatup_nonlinear.jl # nonlinear heatup (10s cap)
Figures save to ../docs/figures/. Reach results save to
../reachability/*.mat (gitignored).
Structure
See CLAUDE.md for the architectural overview and ../journal/ for
the invention-log-style narrative of how this code got written.
Dependencies
From Project.toml:
OrdinaryDiffEq— ODE solver, Rodas5 for stiff systems.MatrixEquations—arecfor LQR Riccati,lyapcfor Lyapunov.ReachabilityAnalysis+LazySets— reach sets and set operations.Plots— figures (GR backend by default).JSON— read../reachability/predicates.json.MAT— save results.
Manifest.toml is gitignored; regenerate locally on first
Pkg.instantiate().