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

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.