Approximating solution of stochastic differential games for distributed control of a water network. Issue 16 (2022)

• Record Type: Journal Article
• Authors: Misra, Rahul; Wisniewski, Rafał; Kallesøe, Carsten S.
• Is Part Of: IFAC-PapersOnLine. Volume 55:Issue 16(2022)
• Page Start: 110
• Page End: 115
• Publication Date: 2022
• Subjects: Stochastic Games -- Stochastic differential equations -- Dynamic programming -- Markov chain approximation -- Water distribution networks; Automatic control -- Periodicals; 629.805
• DOI: 10.1016/j.ifacol.2022.09.009
• Languages: English
• ISSNs: 2405-8963

Abstract

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