Stochastic optimal control for urban water supply and demand management investment

On the basis of logistic (Verhulst) model describing obstruction to a growth of population under environment and resources restriction, the most extensively used urban water demand function, namely, urban average population water demand model was established. For the sake of the extraordinary significance of efficiency and effect of investment in water industry, an urban water supply function was formed based on neoclassical economic theory of investment. Through transforming the nonlinear water demand state function from implicit containing time variable to time-varying linear explicit containing time variable, and considering the stochastic noise disturbance in the process of system operation, the nonlinear urban water demand and supply management dynamic optimization system was transformed into stochastic time-varying linear quadratic optimal control system to be dealt with. By means of reasonable drawing up urban water supply investment decision, the total square of biased deviation of urban water supply and demand can be minimized. Through choosing performance index weighting coefficients when adjusting system parameter on a certain condition, the solution of the Riccati matrix differential equation can be a constant matrix and the system controller design can be simplified.