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

8 Wind speed is Low Surface ocean (𝜉S) is Low No effect 9 Wind speed is High Climate risk High Increase Energy sources 10 Wind speed is Low Climate risk Low Decrease Power output https://doi.org/10.1371/journal.pone.0333846.t001 PLOS One https://doi.org/10.1371/journal.pone.0333846 October 14, 2025 18/ 30

PLOS One Design of global climate control based on fuzzy systems Fig 12. Response of atmospheric (𝜉A) with and without fuzzy rules. https://doi.org/10.1371/journal.pone.0333846.g012 Fig 13. Response of terrestrial biosphere (𝜉T) with and without fuzzy rules. https://doi.org/10.1371/journal.pone.0333846.g013 another suggests that the model’s prediction and the actual temperature are in good agree- ment. A periodic temperature variation that may be impacted by external or control sys- tem elements is suggested by the data’s apparent sinusoidal rhythm. The percentage discrep- ancy between the measured and predicted temperatures is displayed in this graphic. There is a noticeable increase in the error between 4 and 6 seconds, even though it stays minor and steady for the most of the time–line. This implies that the model had trouble correctly pre- dicting the temperature during this time, possibly as a result of abrupt changes in the sur- rounding environment or quick variations. The tight match between the anticipated and mea- sured data in Fig 15 shows how well the model predicts temperature. The steep error spikes in Fig 6 imply that either there was noise in the data during that time period or the model PLOS One https://doi.org/10.1371/journal.pone.0333846 October 14, 2025 19/ 30

PLOS One Design of global climate control based on fuzzy systems Fig 14. Response of Surface ocean (𝜉S) with and without fuzzy rules. https://doi.org/10.1371/journal.pone.0333846.g014 Fig 15. Greenhouse’s interior temperature and the fuzzy model’s prediction. https://doi.org/10.1371/journal.pone.0333846.g015 would have trouble capturing abrupt temperature changes. These might be caused by inac- curate sensors, abrupt changes in the environment, or restrictions in the model’s capacity to make predictions. Although the model works well in general, it might need to be improved in order to lessen the error spikes that are shown at specific times. These disparities might be reduced with the use of strategies like better data filtering, better model tuning, or more feature inclusion. Fig 15 shows that the dynamic model accurately forecasts the temperature outside the greenhouse. The data exhibits a sinusoidal pattern, indicating recurring variations that are probably impacted by environmental cycles like exposure to sunlight, meteorological circum- stances, or temperature regulation systems. There are slight variations between the expected PLOS One https://doi.org/10.1371/journal.pone.0333846 October 14, 2025 20/ 30

PLOS One Design of global climate control based on fuzzy systems Fig 16. The Global climate model’s outcome for internal temperature differ. https://doi.org/10.1371/journal.pone.0333846.g016 Fig 17. Greenhouse’s exterior temperature and the dynamic model’s prediction. https://doi.org/10.1371/journal.pone.0333846.g017 and actual temperatures, especially during the peak and trough periods, which could indicate model flaws or outside disturbances. The temperature trend shows greater variability during periods of peak temperature, suggesting increased sensitivity to external factors like sunlight intensity, wind patterns, or sensor noise. It also generally corresponds with the sinusoidal pat- tern seen in Fig 15, indicating periodic environmental changes. These variations’ fluctuating amplitudes reflect changing environmental conditions. In Figs 17 and 18 show a significant agreement between the predicted and observed values, indicating that the dynamic model accurately and minimally represents the overall temperature trend. In Fig 17’s temperature variability demonstrates how intricate and dynamic the greenhouse’s external environment is. Although the model seems stable, it might be improved to better manage abrupt changes PLOS One https://doi.org/10.1371/journal.pone.0333846 October 14, 2025 21/ 30

PLOS One Design of global climate control based on fuzzy systems Fig 18. The Global climate model’s outcome for internal temperature differ. https://doi.org/10.1371/journal.pone.0333846.g018 (seen as noise in Fig 18) in order to increase prediction accuracy. The dynamic model exhibits a significant association with measured data and accurately forecasts the greenhouse’s outside temperature. Sharp temperature swings, however, imply that the model’s performance might be further enhanced by addressing environmental variability or reducing noise. 6.2 The control cost function u(t) = 𝜓(z(t)) As a control objective, [36] proposes a closed–loop controller that matches the fossil fuel demand to the maximum extent possible while preventing compartmental network over- flows. If there is only one output, then the formula is u(t) = 𝜓(𝜅(t)) , where 𝜓 is as follows: 𝜓 ∶ R+ ↦ R+. No restriction is placed on the notation, throughout the time as it is con- tinuously differentiable and rising gradually, and fulfils the conditions 𝜓(0) = 0 as well as lim𝜅→∞ 𝜓(𝜅) = 1. Using this freedom, the controller could be improved, e.g., by parameter- izing 𝜓 with many tunable parameters. Instead of aiming for maximal simplicity, we chose to represent the imaginary buffer with 𝜅0 = 𝜅max, its initial value. A smooth controller instal- lation was also important to us. As a result, 𝜅 ≥ 𝜅max is equal to 𝜓(𝜅) = 1 . During the time when the buffer is empty and the storage 𝜅 is full, the controller is inactive, but once the buffer

competes and the rest of the storage 𝜅 decreases, the controller becomes active. In Fig 19, the readers can observed the response of atmospheric (𝜉A) in the atmosphere, and land bio- sphere. In addition, the convergence of the control inputs at different values of 𝜓(𝜅(t)) can be observed in Fig 20. Using the mathematical form given above, we can also write the control function in the following way: 𝜓(𝜅) = { g 𝜅 ≤ 𝜅max, 1 𝜅 > 𝜅max, PLOS One https://doi.org/10.1371/journal.pone.0333846 October 14, 2025 22/ 30

PLOS One Design of global climate control based on fuzzy systems Fig 19. Response of atmospheric (𝜉A) in the atmosphere, and land biosphere. https://doi.org/10.1371/journal.pone.0333846.g019 Fig 20. Convergence of the control inputs at different values of 𝜓(𝜅(t)). https://doi.org/10.1371/journal.pone.0333846.g020 In accordance of g with the following requirements: ⎧⎪⎪⎪⎪⎪⎪ ⎨ ⎪⎪⎪⎪⎪⎪⎩ g(0) = 0, g (𝜅max) = 1, g′(0) = 1/𝜅max, g′ (𝜅max) = 0, The coefficients are uniquely determined when a cubic Hermite spline is used to solve the cubic equation. g(𝜅) = 𝛼0 + 𝛼1𝜅1 + 𝛼2𝜅2 + 𝛼3𝜅3. PLOS One https://doi.org/10.1371/journal.pone.0333846 October 14, 2025 23/ 30

PLOS One Design of global climate control based on fuzzy systems Consequently, the controller’s timing is determined only by 𝜅max , which determines when it turns off and at what speed it operates. Controllers with steep slopes can react quickly at low values of 𝜅max, while those with steep slopes at higher values of 𝜅max react slowly. In contrast to original model, we assume that the air–ocean flow (𝜆A→S) and the air–biosphere flow (𝜆A→T) concentrate at 200 and 90 PgC year –1, respectively. The idea that natural sinks are saturated is consistent with previous studies. Controlling fossil fuel emissions can avoid this congestion by allowing emissions to be controlled based on a known demand p. By allowing only a small percentage 𝜓 of the demand p, the authors implement an output feedback control scheme. The auxiliary variable 𝜅 is defined as follows: ̇ 𝜓(t) = y(t) – 𝜓(𝜅)).p(t) (13) where y(t) = 𝜆S→D – 𝜆D→S Carbon flux to the deep ocean is the amount of carbon that leaves the system. y(t) is a measure of the net outflow from the system, which feeds the variable 𝜅. After that, drain by a controlled input whose size is based on the virtual pool’s content via a monotonic and continuous–time differentiable at first input. A function with no constraints 𝜓 is on the other hand. This arrangement prevents congestion 𝜓 as it maintains the total mass constant while generating a physically closed virtual system. Congestion control can be used as an additional goal in a realistic scenario based on the freedom to choose. In terms of some desired prop-

erties, it may be optimized. Since no assumption of optimality is necessary for this example, such optimization is obviously outside its purview. In instances where 𝜅max assumes minimal values, the controller exhibits a pronounced gra- dient, indicating its capacity for rapid response; conversely, as the parameter attains greater magnitudes, the controller demonstrates a more gradual reaction. In the same way, the con- vergence ratio of all trajectories has been shown in Figs 21, 22, and 23. The influence of vary- ing 𝜅max values on the regulatory framework and its efficacy in preventing the buildup of atmospheric carbon within the context of thermal energy storage can be observed in Fig 24. Fig 21. Convergence ratio of 𝜉A(t) and ∥ 𝜉A(t) ∥. https://doi.org/10.1371/journal.pone.0333846.g021 PLOS One https://doi.org/10.1371/journal.pone.0333846 October 14, 2025 24/ 30

PLOS One Design of global climate control based on fuzzy systems Fig 22. Convergence ratio of 𝜉T(t) and ∥ 𝜉T(t) ∥. https://doi.org/10.1371/journal.pone.0333846.g022 Fig 23. Convergence ratio of 𝜉S(t) and ∥ 𝜉S(t) ∥. https://doi.org/10.1371/journal.pone.0333846.g023 The quantity of carbon emissions permitted annually, measured in PgC, as determined by 𝜆F→A(t) = u(t).p(t). The terrestrial biosphere refers to the portion of Earth’s surface that sup- ports life, encompassing all ecosystems on land. It includes forests, grasslands, deserts, tundra, and other terrestrial ecosystems. An essential component of the global carbon cycle is the ter- restrial biosphere, influencing climate regulation, biodiversity, and the provision of ecosystem services such as food, water, and raw materials. From the Fig 25, for low 𝜅max values, the con- troller exhibits a sharp incline, enabling rapid response, whereas for higher parameter values, the controller’s reaction is more gradual. Remark 4. The outputs from y(t) the carbon–climate system are utilized in various ways to inform control strategies and policy decisions. Here are the key areas where these outputs are PLOS One https://doi.org/10.1371/journal.pone.0333846 October 14, 2025 25/ 30

PLOS One Design of global climate control based on fuzzy systems Fig 24. The influence of varying 𝜅max values on the regulatory framework and its efficacy in preventing the buildup of atmospheric carbon within the context of thermal energy storage. https://doi.org/10.1371/journal.pone.0333846.g024 Fig 25. The quantity of carbon emissions permitted annually, measured in PgC, as determined by 𝜆F→A(t) = u(t).p(t). https://doi.org/10.1371/journal.pone.0333846.g025 PLOS One https://doi.org/10.1371/journal.pone.0333846 October 14, 2025 26/ 30

PLOS One Design of global climate control based on fuzzy systems applied for control Input for Feedback Mechanisms; System Identification and Observability, and Policy Evaluation and Adjustment. The outputs from the system, such as measurements of atmospheric CO2 concentrations and surface temperatures, are crucial for closed–loop control systems. These outputs help in adjusting control actions based on real–time data, allowing for adaptive management of the carbon–climate system. Model identification, which entails build- ing mathematical models from observed data, depends on outputs. Understanding the dynamics of the carbon–climate system and evaluating its observability–the capacity to deduce the system’s state from sparse observations are aided by this approach. Monitoring plant’s outputs offer vital data for assessing how well–functioning the policies in place are. Data sharing is applicable to this article as no data–sets were generated or analyzed during the current study. In case of ethical statement, both human and/or animal investigations were not approved for this research. 7 Conclusions It is possible to model Carbon–climate control as a closed–loop issue that continuously modi- fies the system’s activity in response to measurements and uncertainty. In this paper, we pro- vide a new mathematical description of the carbon–climate structure based on fuzzy systems in order to formalize the closed–loop control problem. A compartmentalized representation of the global carbon structure can be used to achieve particular mathematical properties such

as dynamic stability by utilizing the compartmental structure of the system of equations. With our simulation results, the authors demonstrated that fuel requirement and the ability of the plant to transport geological reservoirs for carbon, such as the deep sea, could be effectively managed to manage the global carbon cycle. By analyzing the demand and internal dynam- ics of the system, we obtained a mathematical rule for prescribing actions. This rule can be applied to adaptive carbon cycle management. Unlike scenario–based emission route pre- scriptions, this technique could be useful for policy decisions made on shorter time horizons than those imposed by long–term scenarios. 7.1 Future direction Fuzzy logic is used to model and control the intricacies and uncertainties in climate systems in order to control the global climate based on fuzzy systems with carbon emissions. The complexity and uncertainty of climate models, data quality and availability, scalability issues, interpretability and transparency, integration with other models, and adaptability and evo- lution are some of the limitations of this approach, despite its potential benefits. Fuzzy sys- tems are a useful tool for handling the uncertainties and complexity of climate modeling, but they have a lot of drawbacks. To overcome these constraints, fuzzy logic must be com- bined with other modeling techniques, data quality must be improved, and computer power must be increased. Collaboration between scientists and policymakers is necessary to cre-

ate resilient, open, and flexible systems that can efficiently guide climate action and decision– making. Furthermore, our recently proposed fuzzy approach [39] can be used to improve a few more directions. Additionally, the following T–S models can be used to further improve the efficiency of Carbon–climate control: • Hybrid Approaches: Consider merging state–of–the–art machine learning techniques with T–S models to increase model adaptability and forecast accuracy. • Localized Adaptation: Considering the need for localized T–S models that account for regional climate variations, guaranteeing precise forecasts appropriate for specific locations. PLOS One https://doi.org/10.1371/journal.pone.0333846 October 14, 2025 27/ 30

PLOS One Design of global climate control based on fuzzy systems • Uncertainty Management: Developing trustworthy techniques to measure and control uncertainty in T–S models in order to generate forecasts that are more precise and compre- hensible. • Long–Term Modeling: Research techniques to improve the T–S model’s ability to project the climate over the long run while accounting for the dynamic nature of climate systems. • Socio–Economic Consideration: We can bridge the gap between social dynamics and climate science by incorporating socio-economic factors, human behavior, and policy consequences into T–S models. • Interdisciplinary Collaboration: Fostering communication and collaboration between cli- mate scientists, mathematicians, decision-makers, and other experts to manage the com- plex relationships and challenges associated with the application of the T–S model in climate change modeling. The Takagi–Sugeno Fuzzy Models (T–S models) offer a promising approach to understand- ing climate change dynamics, they are not without challenges. These concerns need to be rec- ognized and addressed in order to ensure that T–S models are used in climate change research in an accurate and significant manner. In Data inaccuracy, high–quality climate data is nec- essary for accurate forecasts, but that data gaps and uncertainties can inject mistakes into the models, reducing the reliability of the results. Similarly, model complexity for the T–S mod- els may involve additional variables and rules due to the complexity of climate systems, which

could impact their accessibility and computational efficacy. For the model complexity, the T– S models may involve more factors and rules due to the complexity of climate systems, which could impact their accessibility and computational efficacy. Author contributions Conceptualization: Shamrooz Aslam. Data curation: Shamrooz Aslam. Formal analysis: Wer-Jer Chang. Funding acquisition: Wer-Jer Chang. Investigation: Wer-Jer Chang, Shamrooz Aslam. Methodology: Wer-Jer Chang, Shamrooz Aslam, Hazrat Bilal, Muhammad Javid Nawaz. Project administration: Saira Naseer. Resources: Saira Naseer, Muhammad Javid Nawaz. Software: Muhammad Hashim Bukhari, Hazrat Bilal. Supervision: Shamrooz Aslam. Validation: Hazrat Bilal. Visualization: Saira Naseer. Writing – original draft: Saira Naseer, Shamrooz Aslam. Writing – review & editing: Shamrooz Aslam, Muhammad Hashim Bukhari, Muhammad Javid Nawaz. PLOS One https://doi.org/10.1371/journal.pone.0333846 October 14, 2025 28/ 30

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