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>
21 lines
781 B
TOML
21 lines
781 B
TOML
authors = ["Dane Sabo <yourstruly@danesabo.com>"]
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[deps]
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CSDP = "0a46da34-8e4b-519e-b418-48813639ff34"
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DynamicPolynomials = "7c1d4256-1411-5781-91ec-d7bc3513ac07"
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HiGHS = "87dc4568-4c63-4d18-b0c0-bb2238e4078b"
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JSON = "682c06a0-de6a-54ab-a142-c8b1cf79cde6"
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JuMP = "4076af6c-e467-56ae-b986-b466b2749572"
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LazySets = "b4f0291d-fe17-52bc-9479-3d1a343d9043"
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LinearAlgebra = "37e2e46d-f89d-539d-b4ee-838fcccc9c8e"
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MAT = "23992714-dd62-5051-b70f-ba57cb901cac"
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MatrixEquations = "99c1a7ee-ab34-5fd5-8076-27c950a045f4"
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OrdinaryDiffEq = "1dea7af3-3e70-54e6-95c3-0bf5283fa5ed"
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Plots = "91a5bcdd-55d7-5caf-9e0b-520d859cae80"
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ReachabilityAnalysis = "1e97bd63-91d1-579d-8e8d-501d2b57c93f"
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SumOfSquares = "4b9e565b-77fc-50a5-a571-1244f986bda1"
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[compat]
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OrdinaryDiffEq = "6.111.0"
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julia = "1.10"
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