This paper, using actual data, establishes a dynamical model of sulfur dioxide pollution and gives an optimal discharge control policy for Osaka city in Japan. From a mass balance of the gas, a linear scalar state equation is obtained. In spite of the simplicity of the model, it can represent the effect of wind speed, inversion layer, diffusion, boundary concentration and discharge intensity of the pollutant sources. Six unknown parameters in the model and system noise variance are identified by maximizing likelihood function by Flexible Polyhedron Search. This makes the model reasonably representative. A quadratic loss function for the control problem is the weighted sum of two terms; the loss caused by the discharge control and the loss due to the air pollution. The wind speed varies at random according to a Markov transition matrix, considering actual emergency control situations. The optimal control policy is obtained by Dynamic Programming, resulting in linear feedback control dependent on the wind speed, involving a Riccati equation. A practical method of the determination of the weighting coefficient in the loss function is proposed. Since the model is a scalar state system, the whole calculation can be performed with a relatively small computer. This ease of computation and the Markov property of the wind speed suggest that the proposed method is applicable to the actual emergency discharge control.
['Hajime Akashi', 'Hiromitsu Kumamoto']
Brief paper: Optimal sulfur dioxide gas discharge control for Osaka city, Japan