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Urban Comprehensive Water Consumption: Nonlinear Control of Production Factor Input Based upon the C-D Function

Author

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  • Kebai Li

    (School of Management Science and Engineering & China Institute of Manufacturing Development, Nanjing University of Information Science & Technology, Nanjing 210044, China)

  • Tianyi Ma

    (School of Management Science and Engineering & China Institute of Manufacturing Development, Nanjing University of Information Science & Technology, Nanjing 210044, China)

  • Tom Dooling

    (Department of Chemistry Physics, University of North Carolina at Pembroke, Pembroke, NC 28372, USA)

  • Guo Wei

    (Department of Mathematics and Computer Science, University of North Carolina at Pembroke, Pembroke, NC 28372, USA)

Abstract

Utilizing the urban water demand function and the Cobb-Douglas (C-D) production function, an economic control model for the multi-input-multi-output (MIMO) nonlinear system was designed and implemented to describe urban comprehensive water consumption, where the urban water demand function was expressed as the product of the number of water users and per capita comprehensive water consumption, and the urban water supply function was expressed as a C-D production function. The control variables included capital investment and labor input for the urban water supply. In contrast to the Solow model, Shell model and aggregate model with renewable labor resources, the proposed model eliminated value constraints on investment and labor input in the state equations and hence avoided the difficulty in applying these models to urban water supply institutions. Furthermore, the feedback linearization control design (FLCD) method was employed to accomplish stability of the system. In contrast to the optimal control method, the FLCD method possesses an explicit solution of the control law and does not require the solution of a two-point boundary value problem of an ordinary differential equation, making the method more convenient for application. Moreover, two different scenarios of urban water consumption, one for the growth period and the other for the decline period, were simulated to demonstrate the effectiveness of the proposed control scheme.

Suggested Citation

  • Kebai Li & Tianyi Ma & Tom Dooling & Guo Wei, 2019. "Urban Comprehensive Water Consumption: Nonlinear Control of Production Factor Input Based upon the C-D Function," Sustainability, MDPI, vol. 11(4), pages 1-19, February.
    • Handle: RePEc:gam:jsusta:v:11:y:2019:i:4:p:1125-:d:207828
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    References listed on IDEAS

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    1. Natali Hritonenko & Yuri Yatsenko, 2013. "Mathematical Modeling in Economics, Ecology and the Environment," Springer Optimization and Its Applications, Springer, edition 2, number 978-1-4614-9311-2, September.
    2. Kebai Li & Tianyi Ma & Guo Wei, 2018. "Multiple Urban Domestic Water Systems: Method for Simultaneously Stabilized Robust Control Decision," Sustainability, MDPI, vol. 10(11), pages 1-22, November.
    3. Qinghua Zhang & Yanfang Diao & Jie Dong, 2013. "Regional Water Demand Prediction and Analysis Based on Cobb-Douglas Model," Water Resources Management: An International Journal, Published for the European Water Resources Association (EWRA), Springer;European Water Resources Association (EWRA), vol. 27(8), pages 3103-3113, June.
    4. Sankar Prasad Mondal & Susmita Roy & Biswajit Das, 2016. "Numerical Solution of First-Order Linear Differential Equations in Fuzzy Environment by Runge-Kutta-Fehlberg Method and Its Application," International Journal of Differential Equations, Hindawi, vol. 2016, pages 1-14, May.
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    Cited by:

    1. Kebai Li & Tianyi Ma & Guo Wei & Yuqian Zhang & Xueyan Feng, 2019. "Urban Industrial Water Supply and Demand: System Dynamic Model and Simulation Based on Cobb–Douglas Function," Sustainability, MDPI, vol. 11(21), pages 1-18, October.

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