Optimal control for urban water resources effective supply investment

On the basis of Logistic model, which describes obstruction to population growth under restrictions of environment and resources, the model of urban average water demand per person is established, and it is also the most extensively used urban water demand function. For the sake of the extraordinary significance of the efficiency and effect of the capital investment in water industry, and on the basis of neoclassical economic theory of investment, an urban water supply function is constructed. Through transforming the nonlinear water demand state function, which does not explicitly contain time variable, into time-varying linear one, which explicitly contains time variable, the nonlinear urban water resources demand and supply management dynamic optimization system is transformed into time-varying linear quadratic optimal control system. By implementing bang-bang control and singular optimal control on the system, the urban water supply investment decision can be reasonably drawn up, and the square error of water resources total supply and demand could be minimized.