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Model Predictive Control (MPC/NMPC) L1-433

Control TheoryReceding horizon controlδ=5 · challengingL_DAG = 4📋 Stub — not mineable
📋

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

Model Predictive Control (MPC/NMPC): MPC/NMPC: solve finite-horizon constrained optimization at each time step, apply first control action. The forward operator produces the measurement through a 3-node primitive DAG (M.mpc.prediction_model…); recovery is posed as a nonlinear_inverse problem. Difficulty tier delta=5 with effective condition number kappa_eff~500; model_plant_mismatch, disturbance_unforeseen set the accuracy floor at the Omega boundary. See the forward_model field for the closed-form equation.

L-DAG

O.iter -> O.qp.nlp_solver -> S.feasibility.constraint_satisfaction
O.iterO.qp.nlp_solverS.feasibility.constraint_satisfaction

Well-posedness W

Existence:
true
Uniqueness:
true
Stability:
conditional
κ:
10000

Existence of the recovered control_sequence_vector 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 ~= 500); model_plant_mismatch dominates the stability cliff; the remaining mismatch parameters contribute higher-order bias terms. Deterministic sets the irreducible data-fidelity floor.

Solvability C

Solver class:
sparse-recovery [QP_solver_for_linear_MPC or NLP_IPOPT_ACADOS_for_NMPC]
Convergence rate q:
2
Complexity:
O(N * n_x ** 3) for QP MPC; O(N * NLP_iter) for NMPC per iteration

Specs (0)

No L2 specs registered yet for this principle.