# American Institute of Mathematical Sciences

August  2019, 24(8): 3667-3687. doi: 10.3934/dcdsb.2018310

## Pollution control for switching diffusion models: Approximation methods and numerical results

 1 Department of Mathematics, Wayne State University, Detroit, MI 48202, USA 2 Department of Mathematics, University of Georgia, Athens, GA 30602, USA 3 Department of Electrical and Computer Engineering, Wayne State University, Detroit, MI 48202, USA

* Corresponding author: George Yin

Received  March 2018 Revised  July 2018 Published  November 2018

Fund Project: This research was supported in part by the Army Research Office under grant W911NF-15-1-0218. The research of Q. Zhang was also supported in part by the Simons Foundation under 235179

This work focuses on optimal pollution controls. The main effort is devoted to obtaining approximation methods for optimal pollution control. To take into consideration of random environment and other random factors, the control system is formulated as a controlled switching diffusion. Markov chain approximation techniques are used to design the computational schemes. Convergence of the algorithms are obtained. To demonstrate, numerical experimental results are presented. A particular feature is that computation using real data sets is provided.

Citation: Caojin Zhang, George Yin, Qing Zhang, Le Yi Wang. Pollution control for switching diffusion models: Approximation methods and numerical results. Discrete & Continuous Dynamical Systems - B, 2019, 24 (8) : 3667-3687. doi: 10.3934/dcdsb.2018310
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##### References:
The control actions in two states
The value functions in two states
The control actions and value functions in two states
The histograms of distributions
Value functions and optimal controls for NO2
Control actions of NO2 on testing set based on optimal strategy
Control actions of NOx on testing set based on optimal strategy
Value functions and optimal controls for 2 dimension system
Value functions and optimal controls for a 4 dimension case
Control actions on testing set based on optimal strategy
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