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 2 Concepts of control theory in the Mitigation of Climate Model Control theory encompasses many concepts, strategies, and techniques involving optimiza- tion ideas. Although optimization concepts have long been applied in areas such as economics (e.g., inflation control) and in recognizing the benefits of mitigating global warming, applica- tions of contemporary control theory to climate systems remain relatively new. In addition, the concepts of optimization were instrumental in the creation of Integrated Assessment Mod- els (IAMs) [27], which can provide optimal prescriptions that can be used as policy responses. Their central tenet is cost–benefit optimization, which incorporates societal costs of climate impacts to maximize social welfare by exploring a space of future emission trajectories with associated environmental effects [28]. Emissions time trajectories offer data for policymakers, but they lack official feedback and corrective procedures grounded in actual observations. Few studies have employed coupled carbon–climate AI models, which is surprising given their significant potential for modeling and managing the global carbon cycle. In contrast to Solar Radiation Management (SRM), which faces significant uncertainties regarding envi- ronmental impacts and may never be fully deployed, substantial progress has been made in reducing emissions and sequestering carbon in long–term reservoirs. To the best of current

knowledge, formal closed–loop control concepts have not been applied within emission trad- ing policy frameworks based on fuzzy model. Furthermore, very few scientific studies have examined feedback regulation processes in the global carbon cycle using similar ideas. Using locally linear sub–models, the data–driven T–S fuzzy identification described above provides a systematic approach to approximating nonlinear systems. We apply this method to the global carbon–climate system in the next section. Specifically, climatic drivers such as greenhouse gas emissions, solar radiation, and biosphere feedbacks serve as fuzzy inputs, while the model’s state variables–carbon reservoirs and surface temperature–are represented as outputs of fuzzy sub–models. The nonlinear dynamics outlined in Eq (1) can thus be expressed within the T–S fuzzy framework. 3 Mathematical representation of the Global Climate Model At any particular point in time domain (t, R), the global carbon–climate system can be rep- resented as a vector s(t) ∈ Rn with components representing carbon levels and temperatures across earth system reservoirs. The function s(t) representing the state at a given time span can be formally articulated as the outcome of a specific organizing 𝟋 ∶ (s0, 𝜈) ↦ s with ini- tial condition s0 ∶= s(t0) and 𝜈(t) denotes the driving signal in term of vector. For instance, one may consider 𝟋 as a representation of the Earth system, incorporating the initial condi- tion s0 along with a set of time–varying driving parameters 𝜈(t) defined over the time span

T = [t0, tmax] and produces the complete evolution of the state s(t) over the time interval T within the overarching carbon–climate model. Although 𝟋 can be expressed in various ways, the authors will confine its definition in this case study to an initial value problem (IVP) for an interconnected set of ordinary differential equations that represent carbon accumulation within Earth reservoirs denoted as ℂE(t), and surface temperatures expressed through block matrices as 𝕋S(t). ̇ s(t) = [̇ ℂE(t) ̇ 𝕋S(t) ] = [ 𝔹(ℂE, 𝕋E, t).ℂE + s(t) f(ℂE, ℝ, t) ] (1) In the next section, the authors will present the new concept of T–S fuzzy model for the climate control plant. PLOS One https://doi.org/10.1371/journal.pone.0333846 October 14, 2025 8/ 30