Robust Economic Control Decision Method of Uncertain System on Urban Domestic Water Supply

Abstract

As China quickly urbanizes, urban domestic water generally presents the circumstances of both rising tendency and seasonal cycle fluctuation. A robust economic control decision method for dynamic uncertain systems is proposed in this paper. It is developed based on the internal model principle and pole allocation method, and it is applied to an urban domestic water supply system with rising tendency and seasonal cycle fluctuation. To achieve this goal, first a multiplicative model is used to describe the urban domestic water demand. Then, a capital stock and a labor stock are selected as the state vector, and the investment and labor are designed as the control vector. Next, the compensator subsystem is devised in light of the internal model principle. Finally, by using the state feedback control strategy and pole allocation method, the multivariable robust economic control decision method is implemented. The implementation with this model can accomplish the urban domestic water supply control goal, with the robustness for the variation of parameters. The methodology presented in this study may be applied to the water management system in other parts of the world, provided all data used in this study are available. The robust control decision method in this paper is also applicable to deal with tracking control problems as well as stabilization control problems of other general dynamic uncertain systems.

Multiple Urban Domestic Water Systems: Method for Simultaneously Stabilized Robust Control Decision

“…change significantly, if we continue to use Equation (19) for the control decisions, this may lead to a situation in which some cities are unable to achieve their control goal of asymptotical stability. When such a situation occurs in the simulation results, for the system with changed parameters, we should use Equation (16) to resolve the m + 1 linear matrix inequalities for V and W, and try to find a new feasible solution for V and W.…”

“…In the supply theory of economics, fixed capital and labor are important production factors (Romer [31]), which play an equally important role in the urban water industry (Spulber and Sabbaghi [32]). Let the urban water supply function be S(t), which can be expressed as (Li and Ma et al [16])…”

“…where K(t) is the fixed capital stock of the urban domestic water supply industry, L(t) is the labor stock, θ i is the capital output coefficient of city i, and λ i is the labor output coefficient of city i. θ i and λ i usually increase with the level of economic and social development. According to the investment and human capital theory in economics (Romer [31]), the state equations of fixed capital stock K(t) and labor stock L(t) in the domestic water supply industry of city i can be written as (Li and Ma et al [16]):…”

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

“…It is easy to verify that the solution of Equation (13) corresponds to that of Equation (12), and that y = 0 corresponds to x = x * , which is an equilibrium point of Equation (13). Therefore, if we want to study the behavior of Equation (12) near the equilibrium point x * , we study precisely the behavior of Equation (13) in the neighborhood of the origin [23].…”

“…In this case, since Equations (12) and (13) have a one-to-one correspondence relationship, we can take the value of the control input variable of Equation 21as…”