Approximating solution of stochastic differential games for distributed control of a water network

In this paper, our objective is to design a distributed optimal control for pumping stations operating in Water Distribution Network (WDN), where we would like satisfy consumer demands with minimum energy consumption. The WDN has been modeled using graph theory and stochastic differential equations. This leads non-zero sum game. We have approximated the solution of aforementioned game Markov chain approximation combined it Shapley's algorithm so as obtain Minimax mixed strategies. can be obtained computation at without any knowledge costs incurred by other stations. Simulation results on water network show convergence an approximate solution.