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

Kebai Li, Tianyi Ma, Tom Dooling and Guo Wei
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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

Sustainability, 2019, vol. 11, issue 4, 1-19

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.

Keywords: urban water consumption; demand function; Cobb-Douglas production function; multi-input-multi-output nonlinear system; feedback linearization (search for similar items in EconPapers)
JEL-codes: O13 Q Q0 Q2 Q3 Q5 Q56 (search for similar items in EconPapers)
Date: 2019
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

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