Design of global climate control based on fuzzy systems with concept of carbon emissions

PLOS One Design of global climate control based on fuzzy systems Algorithm 1 FCC–I: Fuzzy closed-loop carbon–climate control. Given inputs T = {t0, … , tmax}, Δt, initial state 𝜉(t0) = [𝜉0 A, 𝜉0 T, 𝜉0 S ]⊤, demand p(t)≥0, rule base ℜ, membership functions (MFs), flux maps 𝜆●→●(⋅), and constants 𝜆S→D, 𝜆D→S. Choose bounds for tunable Θ = {𝛾1, 𝛾2, 𝜅max, MF thresholds/widths}. 1: Phase 1: Control variable configuration 2: ForAll 𝜃 ∈ Θ do ▷ 𝜃 groups 𝛾1, 𝛾2, 𝜅max, MF cut–points 3: For k = 1, 2, … , Tmax do 4: Randomly draw MF cut–points and 𝜅max from 𝜃-bounds 5: Using current (𝛾1, 𝛾2), compute one-step flux maps: 𝜆A→T = 60(𝜉A/700)𝛾1 , 𝜆A→S = 100(𝜉A/700), 𝜆T→A = 60(𝜉T/3000), 𝜆S→A = 100(𝜉S/1000)𝛾2 6: Build fuzzy antecedents from MFs; fire rules R to get weights; defuzzify → zfuzzy 7: Define controller shape 𝜓(𝜅): 𝜓(𝜅) = ⎧⎪⎪ ⎨ ⎪⎪⎩ g(𝜅), 𝜅 ≤ 𝜅max 1, 𝜅 > 𝜅max where g is cubic Hermite with g(0) = 0, g(𝜅max) = 1, g′(0) = 1/𝜅max, g′(𝜅max) = 0 8: Compute feedback y(t) = 𝜆S→D – 𝜆D→S and buffer update. 𝜅 ← 𝜅 + Δt (y – 𝜓(𝜅) p) 9: Go to previous Step. 10: Phase 2 : Output (Control) Determination 11: Set 𝜓(⋅) and MFs from HL; simulate over [t0, tmax]: 12: for dot = t0, t0 + Δt, … , tmax 13: u(t) ← 𝜓(𝜅(t)); 𝜆F→A(t) ← u(t) p(t) 14: ̇ 𝜉A ← 𝜆T→A + 𝜆S→A – 𝜆A→T – 𝜆A→S + 𝜆F→A 15: ̇ 𝜉T ← 𝜆A→T – 𝜆T→A; ̇ 𝜉S ← 𝜆A→S – 𝜆S→A – 𝜆S→D + 𝜆D→S 16: 𝜉 ← 𝜉 + Δt [̇𝜉A, ̇ 𝜉T, ̇ 𝜉S]⊤ 17: y(t) ← 𝜆S→D – 𝜆D→S; 𝜅 ← 𝜅 + Δt (y – u p) 18: end for 19: Return tuned parameters, trajectories {𝜉(t)}, control u⋆(t), and buffer 𝜅(t)

ordinary differential equations can now be used to describe the model, for t > t0 = 1765. ⎧⎪⎪⎪⎪ ⎨ ⎪⎪⎪⎪⎩ ̇ 𝜉A = 𝜆T→A + 𝜆S→A – 𝜆A→T – 𝜆A→S + 𝜆F→A(t),̇ 𝜉T = 𝜆A→T – 𝜆T→Ȧ 𝜉S = 𝜆A→S – 𝜆S→A – 𝜆S→D + 𝜆D→S (10) As shown in (10) the right–hand side of (9) depends on t and also on the state matrix 𝜉(t) = ⎛ ⎜ ⎝ 𝜉A(t) 𝜉T(t) 𝜉S(t) ⎞ ⎟ ⎠ T . In other words, fluxes between compartments are nonlinearly depen- dent upon the contents of those compartments. Here are the results of Eq (1), assuming 𝔹 = PLOS One https://doi.org/10.1371/journal.pone.0333846 October 14, 2025 17/ 30