Nonlinear Observer Design L1-437
Unclaimed Principle — open for contribution
This Principle is declared in the catalog but has no reference solver, no pinned dataset, and is not registered on-chain. There is no reward pool. Submitting a cert against this Principle today will record the cert for reproducibility but pay zero PWM.
To claim it as a Bounty #7 contribution: open a PR adding (1) a reference solver, (2) ≥1 dataset pinned to IPFS, (3) updates to the L3 manifest with dataset CIDs. After verifier-agent triple-review, the founders' 3-of-5 multisig signs PWMRegistry.register() and the Principle becomes mineable.
Forward model E
Nonlinear Observer Design: Nonlinear observer: estimate state of nonlinear system dx/dt = f(x, u), y = h(x) using high-gain or Luenberger design. The forward operator produces the measurement through a 3-node primitive DAG (S.hgo.high_gain_observer…); recovery is posed as a nonlinear_inverse problem. Difficulty tier delta=5 with effective condition number kappa_eff~200; Lipschitz_constant_violation, output_noise_amplification set the accuracy floor at the Omega boundary. See the forward_model field for the closed-form equation.
L-DAG
Well-posedness W
- Existence:
- true
- Uniqueness:
- true
- Stability:
- conditional
- κ:
- 5000
Existence of the recovered nonlinear_state_estimate is guaranteed within the declared Omega bounds. Uniqueness holds on the measurement-supported subspace; out-of-support modes are controlled by declared priors. Stability is conditionally stable (kappa_eff ~= 200); Lipschitz_constant_violation dominates the stability cliff; the remaining mismatch parameters contribute higher-order bias terms. Gaussian sets the irreducible data-fidelity floor.
Solvability C
- Solver class:
- classical [high_gain_observer or ISS_Lyapunov_based]
- Convergence rate q:
- 2
- Complexity:
- O(n_x * n_y) per time step for observer update per iteration