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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.
Original language | English |
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Book series | IFAC-PapersOnLine |
Volume | 55 |
Issue number | 16 |
Pages (from-to) | 110-115 |
Number of pages | 6 |
ISSN | 2405-8963 |
DOIs | |
Publication status | Published - 1 Jul 2022 |
Event | 18th IFAC Workshop on Control Applications of Optimization, CAO 2022 - Gif sur Yvette, France Duration: 18 Jul 2022 → 22 Jul 2022 |
Conference
Conference | 18th IFAC Workshop on Control Applications of Optimization, CAO 2022 |
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Country/Territory | France |
City | Gif sur Yvette |
Period | 18/07/2022 → 22/07/2022 |
Sponsor | et al., IFAC TC 1.2. Adaptive and Learning Systems, IFAC TC 1.5 Networked Systems, IFAC TC 2.1 Control Design, IFAC TC 2.2. Linear Control Systems, International Federation of Automatic Control (IFAC) - Technical Committee on Optimal Control, TC 2.4 |
Bibliographical note
Funding Information:Financial support from the Poul Due Jensen Foundation (Grundfos Foundation) for this research is gratefully acknowledged.
Publisher Copyright:
Copyright © 2022 The Authors.
Keywords
- Dynamic programming
- Markov chain approximation
- Stochastic differential equations
- Stochastic Games
- Water distribution networks
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SWIFT
Wisniewski, R., Misra, R., Rathore, S. S., Kuskonmaz, B., Jessen, J. F., Andersen, A. O. & Gundersen, J. S.
01/10/2019 → 30/09/2024
Project: Research
Equipment
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Smart Water Infrastructures Laboratory (SWIL)
Jorge Val Ledesma (Operator), Rafal Wisniewski (Manager), Carsten Kallesøe (Operator), Saruch Satishkumar Rathore (Manager), Rahul Misra (Manager), Vishal Sopan Sawant (Manager) & Abhijit Mazumdar (Manager)
Department of Electronic SystemsFacility: Laboratory