The reachable set of a hypersonic entry vehicle — every state it can be driven to under admissible control — is what safety-critical and threat analysis actually need bounded. Computing it exactly means solving a Hamilton–Jacobi–Isaacs equation on a grid, which is exponential in the state dimension and caps out in practice around four or five states. A rigid-body entry vehicle has thirteen before any augmentation.
The approach taken here embeds the hybrid vehicle dynamics into a Banach space of occupation measures, where the problem becomes linear despite the nonlinearity of the flight mechanics. In the thin-atmosphere limit the resulting measure family is not compact: mass concentrates onto a low-dimensional set of trajectories. The aim is to turn that failure of compactness into a profile decomposition — a finite-dimensional skeleton plus a controlled residual — and to use its structure to derive a comparison certificate rather than search for one numerically, so the resulting bound is analytical and verifiable in exact arithmetic.
Three papers, in series:
| # | Title | Adds |
|---|---|---|
| 1 | Certified Analytical Bounds for Multi-Phase Hypersonic Reachable Sets | the embedding, the decomposition, the certificate |
| 2 | Certified Contraction of Reachable Sets under Sequential Telemetry | successive measurements tighten the bound |
| 3 | Probabilistic Reachability Bounds for Multi-Phase Entry under Process and Measurement Noise | unbounded noise, probabilistic guarantees |
- Six degrees of freedom. Attitude and body rates are states; angle of attack and sideslip are outputs of the attitude solution, not commanded quantities. Controls are flap deflections and RCS moments.
- Multi-phase. Vacuum and atmospheric flight, with and without thrust, are modes of a hybrid system. Equilibrium glide, skip-glide and fractional-orbit profiles are then admissible words over that alphabet rather than separate models.
- Hypersonic constraints are load-bearing. Heating rate, dynamic pressure, load factor and integrated heat load define the entry corridor, and the corridor is what makes the state set compact — a hypothesis every result depends on. Real-gas, rarefaction, ablation and aerothermoelastic effects enter as certified envelopes on the vector field.
Early. The manuscripts are section structure. No derivations are written and no results are computed; nothing in them should yet be read as a claim.
The shared bibliography, manuscripts/shared.bib, is
empty and is being assembled by hand — entries are added as sources are read and
their details checked against the published record. The papers therefore build
with no bibliography at present.
cd manuscripts && ./build.sh # all three papers
./build.sh paper1 # one paper
./build.sh watch paper1 # continuous rebuild| Module | Contents |
|---|---|
spectral/ |
Chebyshev–Gauss–Lobatto operators by direct recurrence with the negative-sum trick; Clenshaw–Curtis quadrature; barycentric interpolation |
ultraspherical/ |
Olver–Townsend banded operators and assembly |
thermal/ |
Landau immobilization frame; semi-discrete charring/Stefan solver on the fixed grid |
structures/ |
Variable-rigidity Euler–Bernoulli operator; free-free BCs by null-space projection; modal reduction; integrators |
plates/ |
Mindlin plates, laminate stiffness |
coupling/ |
Quadrature-normalized kernel force transfer |
batch/ |
NumPy/CuPy backend abstraction; batched common-outer-grid integrator; sampling; occupancy model |
atmosphere/ |
US Standard 1976, MSIS thermosphere, ERA5 reanalysis winds |
dynamics/ |
Quaternion attitude kinematics, deformed-surface incidence |
verification/ |
Executable verification tasks |
pip install -e .[dev]
pip install -e .[atmosphere] # optional: MSIS thermosphere
pip install -e .[cuda] # optional: GPU batch backendpytest tests -q # 331 tests
python -m aether.verification # verification tasks -> results/MIT. See LICENSE.