fa45e96fd1
journal/ directory, LaTeX-based, dated entries, callout boxes for
derivations / decisions / dead ends / limitations, plus an \apass{}
macro for in-line markers when a later deep-pass is needed.
Retroactive A-style entries for 2026-04-17 (controllers, linearization,
LQR, operation-mode linear reach, Lyapunov barrier) and 2026-04-20
(predicates restructure into deadbands+safety+invariants, OL-vs-CL
barrier analysis, mode-obligation taxonomy, heatup-rate-as-halfspace,
mode_boundaries, first Julia nonlinear reach attempt).
Both entries include derivations written out in math, dead-ends I
hit, code snippets with commentary, figure embeds, and terminal
output where it changed what we did next. The goal is invention-log
depth — readable 4 years from now without the git history to help.
journal/README.md documents the conventions. journal.tex aggregates
all entries into one PDF via latexmk.
Kept claude_memory/ separate as per earlier agreement — those are
short AI-context notes, different audience.
Co-Authored-By: Claude Opus 4.7 (1M context) <noreply@anthropic.com>
83 lines
3.1 KiB
Julia
83 lines
3.1 KiB
Julia
#!/usr/bin/env julia
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#
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# barrier_compare_OL_CL.jl — head-to-head Lyapunov barrier bounds with
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# and without LQR feedback. Julia port of reachability/barrier_compare_OL_CL.m.
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#
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# Expected: LQR improves every bound by ~20,000x, but bounds stay
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# physically meaningless. Point is to show the ceiling is plant
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# anisotropy, not controller tuning.
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using Pkg
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Pkg.activate(joinpath(@__DIR__, ".."))
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using Printf
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using LinearAlgebra
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using MatrixEquations
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using JSON
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include(joinpath(@__DIR__, "..", "src", "pke_params.jl"))
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include(joinpath(@__DIR__, "..", "src", "pke_th_rhs.jl"))
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include(joinpath(@__DIR__, "..", "src", "pke_linearize.jl"))
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include(joinpath(@__DIR__, "..", "src", "load_predicates.jl"))
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plant = pke_params()
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x_op = pke_initial_conditions(plant)
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pred = load_predicates(plant)
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A, B, B_w, _, _, _ = pke_linearize(plant)
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# LQR gain (same weights as ctrl_operation_lqr).
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Q_lqr = Diagonal([1.0, 1e-3, 1e-3, 1e-3, 1e-3, 1e-3, 1e-3, 1e-2, 1e2, 1.0])
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R_lqr = 1e6 * ones(1, 1)
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X_ric, _, _ = arec(A, reshape(B, :, 1), R_lqr, Matrix(Q_lqr))
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K = (R_lqr \ reshape(B, 1, :)) * X_ric
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A_cl = A - reshape(B, :, 1) * K
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# Shared Qbar — best from the earlier sweep.
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Qbar = Diagonal([1.0, 1e-4, 1e-4, 1e-4, 1e-4, 1e-4, 1e-4, 1.0, 1e2, 1.0])
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w_bar = 0.15 * plant.P0
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delta_entry = [0.01 * x_op[1];
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0.001 .* abs.(x_op[2:7]);
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0.1; 0.1; 0.1]
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inv2 = pred.mode_invariants[:inv2_holds]
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A_inv = inv2.A_poly
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b_inv = inv2.b_poly
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comps = inv2.components
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b_dev = b_inv .- A_inv * x_op
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function run_case(Acase)
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P = lyapc(Matrix(Acase)', Matrix(Qbar))
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Ph = Hermitian(sqrt(Hermitian(P)))
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Phi = inv(Ph)
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mu = minimum(eigvals(Symmetric(Phi * Matrix(Qbar) * Phi)))
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g_bound = sqrt(B_w' * P * B_w)
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c_inv = (2 * w_bar * g_bound / mu)^2
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c_entry = delta_entry' * abs.(P) * delta_entry
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gamma = max(c_inv, c_entry)
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Pinv = inv(P)
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maxima = [sqrt(gamma * (A_inv[k, :]' * Pinv * A_inv[k, :])) for k in 1:size(A_inv, 1)]
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return gamma, maxima, eigvals(Acase)
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end
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gamma_OL, max_OL, eig_OL = run_case(A)
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gamma_CL, max_CL, eig_CL = run_case(A_cl)
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println("\n=== Open-loop vs LQR closed-loop Lyapunov barrier ===")
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@printf " max Re(eig) OL = %.3e CL = %.3e\n" maximum(real.(eig_OL)) maximum(real.(eig_CL))
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@printf " min Re(eig) OL = %.3e CL = %.3e\n" minimum(real.(eig_OL)) minimum(real.(eig_CL))
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@printf " gamma OL = %.3e CL = %.3e (ratio CL/OL = %.3g)\n" gamma_OL gamma_CL gamma_CL/gamma_OL
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println("\n Per-halfspace max |a' dx| on gamma-ellipsoid:")
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@printf " %-22s %-10s %-14s %-14s %-14s %-10s\n" "halfspace" "headroom" "open-loop" "closed-loop" "CL - OL" "ratio"
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for k in 1:size(A_inv, 1)
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ratio = max_CL[k] / max_OL[k]
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@printf " %-22s %10.3f %14.3f %14.3f %+14.3f %10.3gx\n" comps[k] b_dev[k] max_OL[k] max_CL[k] (max_CL[k] - max_OL[k]) ratio
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end
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println("\n Interpretation:")
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println(" - CL < OL on a row => LQR tightens that halfspace.")
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println(" - CL ~= OL => LQR does not help that direction at all.")
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println(" - CL > OL => LQR made that direction WORSE for the barrier.")
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