Optimal Control (LQR) L1-432
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
Optimal Control (LQR): LQR optimal control: find state feedback gain K minimizing infinite-horizon quadratic cost J = integral(x ** T Q x + u ** T R u) dt. The forward operator produces the measurement through a 3-node primitive DAG (M.riccati.algebraic…); recovery is posed as a parameter_estimation problem. Difficulty tier delta=3 with effective condition number kappa_eff~20; model_uncertainty_A_B, Q_R_mistuning 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:
- 500
Existence of the recovered control_gain_matrix 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 ~= 20); model_uncertainty_A_B dominates the stability cliff; the remaining mismatch parameters contribute higher-order bias terms. Deterministic sets the irreducible data-fidelity floor.
Solvability C
- Solver class:
- classical [DARE_Riccati_solver (MATLAB lqr or scipy.signal.lqr)]
- Convergence rate q:
- 2
- Complexity:
- O(n ** 3) for Riccati equation solution per iteration