1{
  2  "seed": 7,
  3  "system": {
  4    "A": 0.2,
  5    "B": 1.0,
  6    "C": 1.0,
  7    "D": 0.0,
  8    "rho": 0.99,
  9    "horizon": 400
 10  },
 11  "math_check": {
 12    "closed_loop_ratio_predicted": 0.5,
 13    "closed_loop_ratio_observed": 0.5,
 14    "max_ratio_error": 0.0
 15  },
 16  "comparison": {
 17    "baseline_L0_gain": 1.0206207261596576,
 18    "idea_L06_gain": 1.6666666666666667,
 19    "idea_certificate_gamma": 5.128535538220312,
 20    "idea_over_baseline_gain_ratio": 1.632993161855452
 21  },
 22  "predictions": {
 23    "boundary_predicted_L": 0.8,
 24    "boundary_observed_first_unstable_L": 0.81,
 25    "boundary_grid_rows": [
 26      {
 27        "L": 0.0,
 28        "empirical_l2_gain": 1.0206207261596576,
 29        "analytic_l2_gain": 1.0206207261596576,
 30        "certificate_gamma": 1.2582154827832464,
 31        "certificate_feasible": true,
 32        "status": "scipy-slsqp",
 33        "stable_analytic": true
 34      },
 35      {
 36        "L": 0.2,
 37        "empirical_l2_gain": 1.0910894511799618,
 38        "analytic_l2_gain": 1.0910894511799618,
 39        "certificate_gamma": 1.680707756725894,
 40        "certificate_feasible": true,
 41        "status": "scipy-slsqp",
 42        "stable_analytic": true
 43      },
 44      {
 45        "L": 0.4,
 46        "empirical_l2_gain": 1.25,
 47        "analytic_l2_gain": 1.25,
 48        "certificate_gamma": 2.5317260923139813,
 49        "certificate_feasible": true,
 50        "status": "scipy-slsqp",
 51        "stable_analytic": true
 52      },
 53      {
 54        "L": 0.6,
 55        "empirical_l2_gain": 1.6666666666666667,
 56        "analytic_l2_gain": 1.666666666666667,
 57        "certificate_gamma": 5.128535538220312,
 58        "certificate_feasible": true,
 59        "status": "scipy-slsqp",
 60        "stable_analytic": true
 61      },
 62      {
 63        "L": 0.75,
 64        "empirical_l2_gain": 3.2025630761017427,
 65        "analytic_l2_gain": 3.202563076101742,
 66        "certificate_gamma": 22.469625350236743,
 67        "certificate_feasible": true,
 68        "status": "scipy-slsqp",
 69        "stable_analytic": true
 70      },
 71      {
 72        "L": 0.79,
 73        "empirical_l2_gain": 7.087646678417917,
 74        "analytic_l2_gain": 7.088812050083354,
 75        "certificate_gamma": 200.5037818054957,
 76        "certificate_feasible": true,
 77        "status": "scipy-slsqp",
 78        "stable_analytic": true
 79      },
 80      {
 81        "L": 0.81,
 82        "empirical_l2_gain": 373.725537945458,
 83        "analytic_l2_gain": Infinity,
 84        "certificate_gamma": NaN,
 85        "certificate_feasible": false,
 86        "status": "scipy-slsqp infeasible",
 87        "stable_analytic": false
 88      },
 89      {
 90        "L": 0.9,
 91        "empirical_l2_gain": 7.1543755041161096e+16,
 92        "analytic_l2_gain": Infinity,
 93        "certificate_gamma": NaN,
 94        "certificate_feasible": false,
 95        "status": "scipy-slsqp infeasible",
 96        "stable_analytic": false
 97      },
 98      {
 99        "L": 1.0,
100        "empirical_l2_gain": 5.910045640679525e+31,
101        "analytic_l2_gain": Infinity,
102        "certificate_gamma": NaN,
103        "certificate_feasible": false,
104        "status": "scipy-slsqp infeasible",
105        "stable_analytic": false
106      },
107      {
108        "L": 1.2,
109        "empirical_l2_gain": 2.0603956252812265e+58,
110        "analytic_l2_gain": Infinity,
111        "certificate_gamma": NaN,
112        "certificate_feasible": false,
113        "status": "scipy-slsqp infeasible",
114        "stable_analytic": false
115      }
116    ],
117    "epsilon_linear_fit_slope": 1.2500000000000007,
118    "epsilon_zero_norm": 0.0,
119    "epsilon_norms": {
120      "0.0": 0.0,
121      "0.25": 0.3125,
122      "0.5": 0.625,
123      "1.0": 1.25,
124      "2.0": 2.5
125    },
126    "epsilon_prediction": "state l2 norm is proportional to one-sample disturbance epsilon",
127    "certificate_prediction": "feasible IQC gamma upper-bounds empirical l2 gain"
128  }
129}