L1 ⚛ L1-433 ⊙ Testnet

Model Predictive Control (MPC/NMPC)

Control Theory · Receding horizon control

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⬇ L1-433.md

# ⚛ L1 Principle — Model Predictive Control (MPC/NMPC) **ID:** `L1-433` · **Status:** ⊙ Testnet (genesis catalog) > **🌐 Domain:** Control Theory — *Receding horizon control* > **🎯 Problem class:** nonlinear inverse · **🧮 Solution space:** control sequence vector > **📡 Carrier:** N/A · **🌫 Noise:** deterministic > **⚖ Difficulty (δ):** 5 · **⛓ Block:** 41555257 --- ## 🧠 1. Introduction **Model Predictive Control (MPC/NMPC)** is a **nonlinear inverse problem** whose unknown lives in **control sequence vector** space, within the **Receding horizon control** sub-domain of **Control Theory**. Measurements consist of N/A via a **receding horizon optimization** sensing mechanism. The forward operator applies, in order: a fixed-point or gradient iteration on the unknown; O · qp · nlp solver operator; S · feasibility · constraint satisfaction operator. Observations are corrupted by no stochastic noise (deterministic measurement). 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. ## ⚙ 2. Forward Model Physical chain: **x** → O · qp · nlp solver → S · feasibility · constraint satisfaction → **y** (detector). ``` y = `S.feasibility.constraint_satisfaction` `O.qp.nlp_solver` x (deterministic) ``` **Measurement DAG:** | Primitive | What it does | |---|---| | `O.qp.nlp_solver` | O · qp · nlp solver operator | | `S.feasibility.constraint_satisfaction` | S · feasibility · constraint satisfaction operator | **🛠 Solver components** _(used inside the solver, not in the forward equation)_: | Primitive | What it does | |---|---| | `O.iter` | A fixed-point or gradient iteration on the unknown | ## 🔬 3. Physics Fingerprint | Property | Value | |---|---| | Domain | Control Theory | | Sub domain | Receding horizon control | | Carrier | N/A | | Problem class | nonlinear_inverse | | Solution space | control_sequence_vector | | Noise model | deterministic | | Integration axis | prediction_horizon | | Difficulty delta | 5 | | L dag | 4 | ## 📡 4. Measurement Model 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. | Metric | Value | |---|---| | Metric | tracking_RMSE_normalized | | Secondary | constraint_violation_rate | ## 📏 5. Operating Range (Ω) **Center problem class:** `nonlinear_inverse` · **Forward operator:** `receding_horizon_optimization` **Center point:** | Parameter | Unit | Value | |---|---|---| | N states | — | 4 | | N constraints | — | 10 | | Prediction horizon n | N | 20 | | Computation budget ms | ms | 100 | **Allowed bounds:** | Parameter | Unit | Range | |---|---|---| | N states | — | 2 – 20 | | N constraints | — | 0 – 50 | | Prediction horizon n | N | 5 – 100 | | Computation budget ms | ms | 1 – 1000 | ## 🎯 6. Tolerance (ε) **Center tolerance:** 0.05 tracking_RMSE_normalized | Metric | Range | |---|---| | Tracking rmse normalized | 0.01 – 0.3 | ## ⚖ 7. Hardness Function Hardness scales as **`epsilon_fn`** on **tracking_RMSE_normalized**, with κ = `10000.0` and δ = `5`. ## 💾 8. Reference Dataset - **primary** · weight 1.0 · IPFS _(not pinned yet)_ ## 9. On-chain Registration - **Chain hash:** `0xb000e1d7a08cc5cb0d4ecc259034584c201fd6de1e1a2a690cd77a869ac31326` - **Chain tx hash:** `0xba5a293fd0f12ab9dfb0d295d8969dc2ae7b014e470ff096eece79b10288d033` - **Chain block:** `41555257` --- ## File Mapping This bundle consists of: `L1-433.md`, `L1-433.json`. | File | Role | How to regenerate | |------|------|-------------------| | `L1-433.md` | Source of truth — edit this | Human or LLM | | `L1-433.json` | Structured metadata for the registry | LLM regenerates from the sections above | **Prompt for your LLM after editing this Markdown:** > Read the attached Markdown. Regenerate the sibling `.json` so every field matches. > Preserve the schema documented in the rows above. > Output each file in its own fenced code block tagged with the filename. > Output only the JSON object. _This Markdown was auto-synthesized from the catalog row for `L1-433`._ _Edit it, regenerate the JSON, and submit at [/submit](/submit) to claim the artifact._

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L2-433-001 Model Predictive Control (MPC/NMPC) — Nominal + Mismatch Specs

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📋 JSON metadata

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  "domain": "Control Theory",
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    "noise_model": "deterministic",
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    "sensing_mechanism": "receding_horizon_optimization",
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    "sub_domain": "Receding horizon control",
    "title": "Model Predictive Control (MPC/NMPC)"
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      "prediction_horizon_N": [
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  },
  "staked_pwm": 0.0,
  "status": "testnet",
  "sub_domain": "Receding horizon control",
  "title": "Model Predictive Control (MPC/NMPC)"
}

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