ABSTRACT
In the last decades, due to the increasingly severe global warming, investments in clean technology, reforestation, and political action have been studied to reduce CO2 emission to help people protect their environment and natural resources in the earth. In this chapter, a nonlinear stochastic system model is introduced to describe the stochastic dynamic system of CO2 emission with control inputs, including clean technology, reforestation, and carbon tax, under stochastic system uncertainties. For the efficient resources management, a robust management control is designed based on the stochastic https://www.w3.org/1998/Math/MathML"> H ∞ https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9780429432941/63df2486-ef31-4a70-9449-3488247ff9a8/content/inline12_1.tif" xmlns:xlink="https://www.w3.org/1999/xlink"/> game strategy to force the dynamic of atmospheric CO2, resources, and GDP tracking a desired reference output specified beforehand. The worst-case effect of stochastic parametric fluctuations, external disturbances, and uncertain initial conditions on the target tracking performance is considered and minimized to achieve the robust tracking from the stochastic https://www.w3.org/1998/Math/MathML"> H ∞ https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9780429432941/63df2486-ef31-4a70-9449-3488247ff9a8/content/inline12_2.tif" xmlns:xlink="https://www.w3.org/1999/xlink"/> game theory perspective. This stochastic https://www.w3.org/1998/Math/MathML"> H ∞ https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9780429432941/63df2486-ef31-4a70-9449-3488247ff9a8/content/inline12_3.tif" xmlns:xlink="https://www.w3.org/1999/xlink"/> game management strategy design problem, in which one player (stochastic uncertainties) maximizes the tracking error and another player (management control strategy) minimizes the tracking error, could be equivalent to a robust minimax tracking problem of resource management control for CO2 emission and reduction of greenhouse effect. To avoid solving the Hamilton–Jacobi–Issac inequality (HJII) of nonlinear https://www.w3.org/1998/Math/MathML"> H ∞ https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9780429432941/63df2486-ef31-4a70-9449-3488247ff9a8/content/inline12_4.tif" xmlns:xlink="https://www.w3.org/1999/xlink"/> stochastic game problem for robust management control strategy, a fuzzy model is proposed to approximate the nonlinear CO2 emission model to simplify the design procedure of robust management control strategy. Then the nonlinear stochastic https://www.w3.org/1998/Math/MathML"> H ∞ https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9780429432941/63df2486-ef31-4a70-9449-3488247ff9a8/content/inline12_5.tif" xmlns:xlink="https://www.w3.org/1999/xlink"/> game problem of robust resource management control could be easily solved by fuzzy stochastic game approach via LMI technique in Matlab Toolbox.
