`pid_stability_one_statement`

proved

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module: IndisputableMonolith.Robotics.PIDStabilityFromJCost
domain: Robotics
line: 172 · github
papers citing: none yet

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IndisputableMonolith.Robotics.PIDStabilityFromJCost on GitHub at line 172.

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formal source

 169
 170/-! ## §7. One-statement summary -/
 171
 172theorem pid_stability_one_statement :
 173    ∀ (f : ℝ → ℝ), RecognitionDescent f →
 174      f 1 = 1 ∧
 175      (∀ (r : ℝ), 0 < r → r ≠ 1 → Cost.Jcost (f r) < Cost.Jcost r) ∧
 176      (∀ (x : ℝ), 0 < x → (Cost.Jcost x = 0 ↔ x = 1)) := by
 177  intro f hf
 178  refine ⟨hf.fixes_equilibrium, ?_, ?_⟩
 179  · intro r hr hne
 180    exact hf.strict_descent_off r hr hne
 181  · intro x hx
 182    exact cost_zero_iff_equilibrium hx
 183
 184end
 185
 186end PIDStabilityFromJCost
 187end Robotics
 188end IndisputableMonolith

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