02a675c152
Stand up reachability/ with a hand-rolled zonotope propagator for linear closed-loop systems (reach_linear.m: axis-aligned box hull, augmented-matrix integration for the disturbance convolution). Use it in reach_operation.m to discharge the operation-mode safety obligation: from a +/-0.1 K box on T_avg, under Q_sg in [85%, 100%]*P0, LQR keeps T_c within 0.03 K of setpoint over 600 s. Safety band is +/-5 K, so the obligation is satisfied with five orders of margin. barrier_lyapunov.m attempts the analytic counterpart via a weighted Lyapunov function. Sweeping the Qbar(T_c) weight, the best quadratic barrier allows ~33 K deviation on the gamma level set — still outside the 5 K safety band. This is a fundamental limitation of quadratic barriers for anisotropic safety specs (thin-slab safe set in a precursor-heavy state space). Documented in the file: next step for a tight analytic certificate is SOS polynomial or polytopic barrier, which need solvers we don't have locally yet. reach_linear.m started out with a halfwidth-propagation bug (signed A_step instead of |A_step|); fixed before commit after noticing the reach envelope exactly matched the initial box on T_c. Figures saved to docs/figures/. .mat result files gitignored — they are regenerated in <1s. Hacker-Split: first end-to-end per-mode reachability artifact. Co-Authored-By: Claude Opus 4.7 (1M context) <noreply@anthropic.com>
56 lines
2.0 KiB
Markdown
56 lines
2.0 KiB
Markdown
# Reachability
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Continuous-mode verification for the PWR_HYBRID_3 hybrid controller.
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## Status
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**Per-mode only.** Following the compositionality argument in the thesis:
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verify each continuous mode separately, let the DRC handle discrete
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switching. Current focus: **operation mode** under LQR feedback.
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## What's here
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- `linearization_at_op.mat` — A, B, B_w and reference point, generated by
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`../plant-model/test_linearize.m`.
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- `reach_linear.m` — box-zonotope propagation of the closed-loop linear
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model under bounded disturbance. Pure MATLAB, no external toolbox.
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- `barrier_lyapunov.m` — Lyapunov-ellipsoid barrier certificate for the
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closed-loop linear system. Solves a Lyapunov equation, reports the
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smallest sub-level set containing the initial set and closed under
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the disturbance.
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- `reach_operation.m` — end-to-end operation-mode reach: linearize at
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x_op, compute LQR gain, propagate zonotope reach set, check against
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the `t_avg_in_range` predicate.
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- `figures/` — generated plots.
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## Running
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From MATLAB:
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```matlab
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cd reachability
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reach_operation % computes reach set + plots
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barrier_lyapunov % solves Lyapunov, reports invariant ellipsoid
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```
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## Tool choice
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Currently using a hand-rolled zonotope reach because:
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- Avoids a ~0.5 GB CORA install for a first-pass result.
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- Linear reach with bounded disturbance has a clean analytic form
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(matrix exponential on the state, integral of e^(A(t-s))·B_w·w ds
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for the disturbance).
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- Stays inside MATLAB, which is where the plant model lives.
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If we need nonlinear reach (and we will, for non-LQR controllers or
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larger reach sets where linearization error matters), the planned
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options are CORA (MATLAB) or JuliaReach (port the plant to Julia).
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## What this does NOT do yet
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- Nonlinear reach for the original P controller on operation.
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- Heatup reach (the ramped reference makes x* time-varying — needs
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trajectory-LQR or a different formulation).
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- Shutdown, scram, initialization reach.
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- Hybrid-system level verification (mode switching validity).
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