1{
  2  "seed": 2915,
  3  "model": "scalar stable nonlinear plant with phi_gamma(x)=gamma*tanh(x), P=1, C=1",
  4  "math": {
  5    "a": 1.0,
  6    "observer_gain": 0.5,
  7    "rho": "gamma",
  8    "alpha": "gamma^2",
  9    "certificate_at_eps_gamma": "M=-2*(a+L)+4*gamma",
 10    "predicted_certificate_boundary_gamma": 0.75,
 11    "predicted_exact_local_boundary_gamma": 1.5
 12  },
 13  "bound_check": {
 14    "rho_theory": 1.7,
 15    "rho_sample_max": 1.6856403581609258,
 16    "alpha_theory": 2.8899999999999997,
 17    "alpha_sample_max": 2.8413834170608943,
 18    "bounds_hold": true
 19  },
 20  "boundary_sweep": {
 21    "predicted_certificate_boundary": 0.75,
 22    "observed_certificate_sign_grid_gamma": 0.8,
 23    "predicted_exact_local_boundary": 1.5,
 24    "observed_exact_local_boundary": 1.5,
 25    "rows": [
 26      {
 27        "gamma": 0.0,
 28        "M": -2.0,
 29        "contracted": true,
 30        "final_abs_error": 1.2325345334126954e-05
 31      },
 32      {
 33        "gamma": 0.1,
 34        "M": -2.5999999999999996,
 35        "contracted": true,
 36        "final_abs_error": 2.6669364910275975e-05
 37      },
 38      {
 39        "gamma": 0.2,
 40        "M": -2.1999999999999997,
 41        "contracted": true,
 42        "final_abs_error": 5.753929905961615e-05
 43      },
 44      {
 45        "gamma": 0.30000000000000004,
 46        "M": -1.7999999999999996,
 47        "contracted": true,
 48        "final_abs_error": 0.00012371847081870573
 49      },
 50      {
 51        "gamma": 0.4,
 52        "M": -1.4,
 53        "contracted": true,
 54        "final_abs_error": 0.0002649381376100109
 55      },
 56      {
 57        "gamma": 0.5,
 58        "M": -1.0,
 59        "contracted": true,
 60        "final_abs_error": 0.0005645946025852013
 61      },
 62      {
 63        "gamma": 0.6000000000000001,
 64        "M": -0.5999999999999996,
 65        "contracted": true,
 66        "final_abs_error": 0.0011960280402718135
 67      },
 68      {
 69        "gamma": 0.7000000000000001,
 70        "M": -0.19999999999999973,
 71        "contracted": false,
 72        "final_abs_error": 0.0025149237900349746
 73      },
 74      {
 75        "gamma": 0.8,
 76        "M": 0.2000000000000003,
 77        "contracted": false,
 78        "final_abs_error": 0.005238484502105017
 79      },
 80      {
 81        "gamma": 0.9,
 82        "M": 0.6000000000000001,
 83        "contracted": false,
 84        "final_abs_error": 0.010777303443079332
 85      },
 86      {
 87        "gamma": 1.0,
 88        "M": 1.0,
 89        "contracted": false,
 90        "final_abs_error": 0.02180294320185896
 91      },
 92      {
 93        "gamma": 1.1,
 94        "M": 1.4000000000000004,
 95        "contracted": false,
 96        "final_abs_error": 0.043071333794499796
 97      },
 98      {
 99        "gamma": 1.2000000000000002,
100        "M": 1.8000000000000007,
101        "contracted": false,
102        "final_abs_error": 0.0821543213074896
103      },
104      {
105        "gamma": 1.3,
106        "M": 2.2,
107        "contracted": false,
108        "final_abs_error": 0.14866262209584083
109      },
110      {
111        "gamma": 1.4000000000000001,
112        "M": 2.6000000000000005,
113        "contracted": false,
114        "final_abs_error": 0.24934919525635033
115      },
116      {
117        "gamma": 1.5,
118        "M": 3.0,
119        "contracted": false,
120        "final_abs_error": 0.3799753436001856
121      },
122      {
123        "gamma": 1.6,
124        "M": 3.4000000000000004,
125        "contracted": false,
126        "final_abs_error": 0.5246809863124708
127      },
128      {
129        "gamma": 1.7000000000000002,
130        "M": 3.8000000000000007,
131        "contracted": false,
132        "final_abs_error": 0.6675106189902515
133      },
134      {
135        "gamma": 1.8,
136        "M": 4.2,
137        "contracted": false,
138        "final_abs_error": 0.8007194816329817
139      },
140      {
141        "gamma": 1.9000000000000001,
142        "M": 4.6000000000000005,
143        "contracted": false,
144        "final_abs_error": 0.9231093368791489
145      },
146      {
147        "gamma": 2.0,
148        "M": 5.0,
149        "contracted": false,
150        "final_abs_error": 1.0360447636667052
151      },
152      {
153        "gamma": 2.1,
154        "M": 5.4,
155        "contracted": false,
156        "final_abs_error": 1.1413245655791728
157      },
158      {
159        "gamma": 2.2,
160        "M": 5.800000000000001,
161        "contracted": false,
162        "final_abs_error": 1.2405096610805566
163      }
164    ]
165  },
166  "rate_sweep": [
167    {
168      "gamma": 0.0,
169      "certificate_upper_bound_logV_slope": -2.0,
170      "observed_logV_slope": -2.9999999999998694,
171      "bound_holds": true
172    },
173    {
174      "gamma": 0.2,
175      "certificate_upper_bound_logV_slope": -2.1999999999999997,
176      "observed_logV_slope": -2.600002133424236,
177      "bound_holds": true
178    },
179    {
180      "gamma": 0.5,
181      "certificate_upper_bound_logV_slope": -1.0,
182      "observed_logV_slope": -2.0000095768029373,
183      "bound_holds": true
184    },
185    {
186      "gamma": 0.8,
187      "certificate_upper_bound_logV_slope": 0.2000000000000003,
188      "observed_logV_slope": -1.400029774007129,
189      "bound_holds": true
190    },
191    {
192      "gamma": 1.0,
193      "certificate_upper_bound_logV_slope": 1.0,
194      "observed_logV_slope": -1.0000611689791186,
195      "bound_holds": true
196    },
197    {
198      "gamma": 1.2,
199      "certificate_upper_bound_logV_slope": 1.7999999999999998,
200      "observed_logV_slope": -0.6001268505573438,
201      "bound_holds": true
202    },
203    {
204      "gamma": 1.4,
205      "certificate_upper_bound_logV_slope": 2.5999999999999996,
206      "observed_logV_slope": -0.20027019585083689,
207      "bound_holds": true
208    }
209  ],
210  "gain_sweep": {
211    "predicted_min_gain_for_kappa_0.8": 1.7999999999999998,
212    "observed_grid_min_gain": 1.8,
213    "rows": [
214      {
215        "gain": 0,
216        "certificate_kappa": -2.8,
217        "meets_target": false
218      },
219      {
220        "gain": 0.1,
221        "certificate_kappa": -2.5999999999999996,
222        "meets_target": false
223      },
224      {
225        "gain": 0.2,
226        "certificate_kappa": -2.4,
227        "meets_target": false
228      },
229      {
230        "gain": 0.3,
231        "certificate_kappa": -2.1999999999999997,
232        "meets_target": false
233      },
234      {
235        "gain": 0.4,
236        "certificate_kappa": -2.0,
237        "meets_target": false
238      },
239      {
240        "gain": 0.5,
241        "certificate_kappa": -1.7999999999999998,
242        "meets_target": false
243      },
244      {
245        "gain": 0.7,
246        "certificate_kappa": -1.4,
247        "meets_target": false
248      },
249      {
250        "gain": 1.0,
251        "certificate_kappa": -0.7999999999999998,
252        "meets_target": false
253      },
254      {
255        "gain": 1.5,
256        "certificate_kappa": 0.20000000000000018,
257        "meets_target": false
258      },
259      {
260        "gain": 1.8,
261        "certificate_kappa": 0.7999999999999998,
262        "meets_target": true
263      },
264      {
265        "gain": 2.0,
266        "certificate_kappa": 1.2000000000000004,
267        "meets_target": true
268      }
269    ]
270  },
271  "noisy_comparison": {
272    "baseline_no_observer": {
273      "mean_mse": 0.0012980416654828559,
274      "std_mse": 0.0
275    },
276    "certified_observer": {
277      "mean_mse": 2.4163893171045498e-05,
278      "std_mse": 1.0999791075781146e-05
279    }
280  }
281}