Optimal control model of urban water resources supply and demand management

Owing to the significance of urban water resources demand management, and in accordance with urban water demand with features of both growth and periodicity, an urban water resources supply and demand management dynamic optimal control model was constructed. On the basis of the prediction of urban water demand, the urban water demand could be satisfied through reasonable control of urban water supply investment. Under state space constraint, a complementary slackness stronger form, required by the method of applying maximum principle to solving optimal control problem, was analyzed not always to be true on the conjoint point where optimal trajectory changes from active into inactive. Then, the normal form of complementary slackness condition should be applied to solving the problem under the circumstances. By implemented singular optimal control on the system, the total square of deviation of urban water resources supply and demand could be minimized in the period of urban water demand growth.