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.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.