Abstract
With the increasingly severe global warming, investments in clean technology, reforestation and political action have been studied to reduce CO2 emission. In this study, a nonlinear stochastic model is proposed to describe the dynamics of CO2 emission with control inputs: clean technology, reforestation and carbon tax, under stochastic uncertainties. For the efficient resources management, a robust tracking control is designed to force resources tracking a desired reference output. The worst-case effect of stochastic parametric fluctuations, external disturbances and uncertain initial conditions on the tracking performance is considered and minimized from the dynamic game theory perspective. This stochastic game problem, in which one player (stochastic uncertainty) maximizes the tracking error and another player (control input) minimizes the tracking error, could be equivalent to a robust minimax tracking problem. To avoid solving the HJI, a fuzzy model is proposed to approximate the nonlinear CO2 emission model. Then the nonlinear stochastic game problem could be easily solved by fuzzy stochastic game approach via LMI technique.
Highlights
In recent years, the world has attracted much attention to environmental issues such as atmospheric pollution, conservation of water reserves and the reduction of tropical forests cover
A nonlinear stochastic model is proposed to describe the dynamics of CO2 emission with control inputs: clean technology, reforestation and carbon tax, under stochastic uncertainties
In order to reduce the emissions of greenhouse gases (GHG), especially CO2, without limiting economic growth, substantial investments should target the development of clean technology, expansion of forested areas and some political actions [4,5,6]
Summary
The world has attracted much attention to environmental issues such as atmospheric pollution, conservation of water reserves and the reduction of tropical forests cover. Caetano et al (2008) [3] follows the ideas in Stollery [15] and offers a quantitative tool for the efficient allocation of resources to reduce the greenhouse effect caused by CO2 emission Their approach was developed by a mathematical model to describe the dynamic relation of CO2 emission with investment in reforestation and clean technology, and propose a method to efficiently manage the available resources by casting an optimal control problem. The parametric fluctuations, external disturbances and uncertain initial conditions are considered as one player to maximize the tracking error, while the control of resource management is considered as another player to minimize the tracking error, from the dynamic game (minimax) theory perspective This stochastic game problem could be equivalent to a robust minimax tracking problem, to achieve a prescribed reference output, in spite of the worst-case effect of parametric fluctuations, external disturbances and uncertain initial condition. Theorem 1: The stochastic game problem in (16) for robust tracking control of stochastic CO2 emission system could be solved by the following minimax tracking control u and the worst-case disturbance v u
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