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.

Highlights

  • China has a great shortage of water resources

  • The existing literature has paid little attention to the following situation: The nonlinear system of urban comprehensive water consumption is composed of the water demand function and the water supply function, where the former is described based on per capita comprehensive water consumption, and the latter is described by the C-D production function

  • From an economic management point of view, this paper studies production factor input control of urban comprehensive water consumption systems

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Summary

Introduction

China has a great shortage of water resources. According to the world development indicators issued by the World Bank in 2017, China’s renewable internal freshwater resources per capita was 2062 m3 in 2014, which was only 35% of the world average of 5917 m3 in that same year [1]. The existing literature has paid little attention to the following situation: The nonlinear system of urban comprehensive water consumption is composed of the water demand function and the water supply function, where the former is described based on per capita comprehensive water consumption, and the latter is described by the C-D production function This comprises the main study of this paper. From an economic management point of view, this paper studies production factor input control of urban comprehensive water consumption systems. In order to avoid difficulties in the application of the optimal control method, this paper adopted the feedback linearization control design method to achieve the stable supply and demand of the urban comprehensive water consumption system.

Economic Control Model for Urban Comprehensive Water Consumption
Consumption Compared with the Existing Economic Dynamics Models
Case Simulation
Findings
Calculate
Full Text
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