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

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 to completely replace combustion processes. Hence, 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 designed 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 tolerates for 6 days the combustion taking place in 5,000 vehicles and in 10,000 house heating systems, it meets the net-zero target, and it nullifies the extraction of finite natural resources. The tropospheric temperature with closed-loop reaches the equilibrium at 133 {\deg}C after 16.4 years; while such an high value requires to further investigate with climate experts the model of the dynamics of the temperature, this work is a first step in designing optimal network control systems for climate stability. Source code is publicly available.