# Эксперимент: IQC-Certified Training Dynamics (#1072)

{
  "worked": true,
  "confidence": 8,
  "verdict": "Built a scalar IQC-certified feedback-dynamics MVP with lifted LMI construction, numerical certification, and reproducible parameter sweeps. The mechanism manifested: the predicted stability boundary L*=1-A=0.8 was observed between L=0.79 (stable) and L=0.81 (unstable), while disturbance sensitivity scaled exactly linearly with epsilon. The certificate was feasible on stable grid points and infeasible on unstable points, although conservative near the boundary.",
  "metrics": {
    "baseline": "No-feedback L=0: empirical finite-horizon state gain 1.0206.",
    "idea": "Feedback L=0.6: empirical gain 1.6667 and IQC certificate gamma 5.1285, or 1.633x the baseline gain. Predicted boundary L*=0.8; observed transition [0.79,0.81]. At L=0.4, epsilon values [0,.25,.5,1,2] produced state norms [0,.3125,.625,1.25,2.5], with fitted slope 1.25 exactly matching the analytic gain."
  },
  "how_to_run": "/home/maxwelhelp/main/bin/python3 iqc_experiment.py",
  "files": [
    "iqc_experiment.py",
    "results.json"
  ],
  "limitations": "This is a scalar toy realization, not a learned optimizer or d=20 finite-sum regression meta-training experiment. The certificate uses fixed rho=0.99 and a bounded SciPy SLSQP fallback because CVXPY was unavailable; its gamma is conservative and should be independently checked with a production SDP solver. No generalization-error or wall-clock comparison was tested."
}