Input-output dynamic model for optimal environmental pollution control |
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| Institution: | 1. School of Science, Nanjing University of Science and Technology, Nanjing, Jiangsu 210094, China;2. Department of Public Basic Courses, Nanjing Institute of Industry Technology, Nanjing, Jiangsu 210023, China;1. Department of Electrical Engineering, International Islamic University, Islamabad, Pakistan;2. Department of Electrical and Computer Engineering, COMSATS University Islamabad, Attock Campus, Attock, Pakistan;3. Future Technology Research Center, National Yunlin University of Science and Technology, 123 University Road, Section 3, Douliou, Yunlin 64002, Taiwan, R.O.C.;4. Department of Electrical Engineering, Institute of Engineering, Polytechnic of Porto, Porto, Portugal;2. Department of Mathematics, SRM Institute of Science & Technology, Chennai 603 203, India;1. School of Astronautics, Beihang University, Beijing 100083, China;2. Beijing Advanced Innovation Center for Big Date-based Precision Medicine, Beihang University, Beijing 100083, China;1. Department of Chemical and Materials Engineering, School of Engineering and Digital Sciences, Nazarbayev University, Nur-Sultan, Kazakhstan;2. Department of Heat Power Setups, Faculty of Energy and Electrical Engineering, Chuvash State University, Cheboksary, Russian Federation;3. Department of Mathematics, School of Sciences and Humanities, Nazarbayev University, Nur-Sultan, Kazakhstan;1. School of Mechanical Engineering, Hangzhou Dianzi University, Hangzhou, China;2. The State Key Laboratory of Fluid Power and Mechatronic Systems, Zhejiang University, Hangzhou, China;3. School of Mechanical and Energy Engineering, Zhejiang University of Science and Technology,Hangzhou, China |
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| Abstract: | This paper describes the allocation of a wastewater treatment fund within a region based on a dynamic input-output model. Considering the complexity of the input-output process, many indeterminate factors must be included in the model. For example, with the aging of machines, an unexpected loss will be caused by the retention of raw materials during an operation; this can be realistically considered as a random variable, because of the sufficiently large amount of historical data. By contrast, actions such as a temporary transfer or inexperienced operators can only be regard as uncertain variables, because of a lack of historical data. First, the pollution control model is formulated in an uncertain environment by including both human uncertainty and objective randomness. Second, an optimal control model subject to an uncertain random singular system is established; this model can be transformed into an equivalent optimization problem. To solve such a problem, recurrence equations are presented based on Bellman’s principle, and these were successfully applied to address the optimal control problem in two special cases. Moreover, two algorithms are formulated for solving the pollution control problem. Finally, the optimal distribution strategies of the pollution control fund used to control the emissions of COD and NH3-H, which are two indicators of wastewater in China, were obtained through the proposed algorithms. |
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