CarboNet: A Finite-Time Combustion-Tolerant Compartmental Network for Tropospheric Carbon Control

TL;DR

CarboNet presents a finite-time combustion-tolerant compartmental network for tropospheric $CO_2$ control, enforcing nonnegativity of all state masses and formulating centralized, linear-quadratic regulators to drive the urban CO$_2$ mass to a pre-industrial reference while meeting a net-zero target. It couples a four-state network with a nonlinear tropospheric temperature model and a circularity metric to quantify resource circularity, deriving both full-state and static output-feedback LQR designs. Numerical results show full-state control reaches the pre-industrial CO$_2$ level in about 25 days (tolerating combustion for about 6 days), while output-feedback takes about 60 days, with the mean tropospheric temperature stabilizing near 13.5 $^\circ$C under closed-loop regulation. These findings illustrate a principled, controllable pathway to climate stability through a centralized network approach and provide publicly available source code for reproducibility.

Abstract

While governments and international organizations have set the net-zero target to prevent a climate event horizon, practical solutions are lacking mainly because of the impracticability in completely replacing combustion processes. To address the net-zero target problem, in this paper we first design a compartmental network whose states must remain in the nonnegative orthant for physical consistency and in which the carbon dioxide emissions result from the combustion of diesel in vehicles and gas in house heaters. Then, we design both full-state and output-feedback linear-quadratic regulators of the compartmental network to bring the mass of carbon dioxide to the pre-industrial era, which is reached in approximately 25 and 60 days, respectively. The output-feedback controller tolerates for 6 days the combustion taking place in 5,000 vehicles and in 10,000 house heating systems, meets the net-zero target, and nullifies the extraction of finite natural resources. With closed-loop control, the tropospheric temperature stabilizes approximately to the pre-industrial era reference condition, i.e., to 13.5 °C, which is 21.7 °C lower than the steady-state temperature achieved without carbon capture. This work is a first step in designing optimal network control systems for climate stability. Source code is publicly available.

Figures (7)

• Figure 1: Compartmental diagraph of the system for tropospheric carbon regulation. It can be represented as the set of compartments $\mathcal{N}_\text{c}$ (\ref{['eq:setNc']}).
• Figure 2: Closed-loop state and control input with full-state feedback and arbitrary rate constants $a_{k,s}$.
• Figure 3: Closed-loop state and control input with full-state feedback for tropospheric $\text{CO}_2$ control.
• Figure 4: Key variables with full-state feedback: (left) circularity, $\phi_1$, and $\phi_\text{nz}$; (middle) tropospheric temperature with open and closed loops; (right) emissivity.
• Figure 5: Closed-loop state, output, and control input with output-feedback gain computed via the Newton's method ilka2022novel in the case of arbitrary rate constants $a_{k,s}$.

Theorems & Definitions (1)

• Definition 1: zocco2025cirl