Abstract
This article describes the design of distributed LQ controllers based on a linear model of a water delivery canal. According to a distributed strategy, a local control agent is associated to each gate of the canal. The main goal is to control the position of the gates in order to drive the water levels for each pool to variable references. For this purpose, local optimization problems are presented, that will be solved at each local controller. In order to achieve a consensus between agents, a coordination method, based on game theory, is presented, including its convergence analysis. The overall controller architecture is described. Simulations, illustrating scenarios in which the convergence conditions are satisfied, are presented.
This work was performed within the framework of the project HARMONY, Distributed Optimal Control for Cyber-Physical Systems Applications, financed by FCT under contract AAC n2/SAICT/2017 - 031411, project IMPROVE - POCI-01-0145-FEDER-031823, and pluriannual INESC-ID funding UIDB/50021/2020.
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References
Mareels, I., Weyer, E., Ooi, S.K., Cantoni, M., Li, Y., Nair, G.: Systems engineering for irrigation systems: successes and challenges. In: Proceedings of the 16th IFAC World Congress (2005)
Litrico, X., Fromion, V.: Modeling and Control of Hydrosystems. Springer (2009)
Cantoni, M., Weyer, E., Li, Y., Ooi, S.K., Mareels, I., Ryan, M.: Control of large-scale irrigation networks. In: Proceedings of the IEEE, vol. 95, no. 1, pp. 75–91 (2007)
Lemos, J.M., Pinto, L.F., Rato, L.M., Rijo, M.: Distributed LQG control of a water delivery canal with feedforward from measured consumptions. In: 20th Mediterranean Conference on Control & Automation, pp. 722–727 (2012)
Lemos, J.M., Pinto, L.: Distributed linear-quadratic control of serially chained systems. IEEE Control Syst. Mag., 26–38 (2012)
Igreja, J.M., Lemos, J.M., Cadete, F.M., Rato, L.M., Rijo, M.: Control of a water delivery canal with cooperative distributed MPC. In: American Control Conference, pp. 3346–3351 (2012)
Mosca, E.: Optimal, Predictive, and Adaptive Contro. Prentice Hall (1995)
Maciejowski, J.M.: Predictive Control with Contraints. Prentice Hall (2002)
Maestre, J.M., Muñoz de la Peña, D., Camacho, E.F.: Distributed model predictive control based on a cooperative game. Optim. Control Appl. Meth. 32, 153–176 (2011)
Mota, J.F.C., Xavier, J.M.F., Aguiar, P.M.Q., Püschel, M.: Distributed ADMM for model predictive control and congestion control. In: 51st IEEE Conference on Decision and Control, pp. 5110–5115 (2012)
Mota, J.F.C.: Communication-Efficient Algorithms For Distributed Optimization. Ph.D. Thesis. Instituto Superior Técnico and Carnegie Mellon University (2013)
Zhong**, J., Yuandan, L., Yuan, W.: Nonlinear small-gain theorems for discrete-time large-scale systems. In: Proceedings of the 27th Chinese Control Conference, pp. 16–18 (2008)
Jiang, Z.P., Wang, Y.: Small gain theorems on input-to-output stability. In: Proceedings of the 3rd International DCDIS Conference, pp. 220–224 (2003)
Jiang, Z., Wang, Y.: Input-to-state stability for discrete-time nonlinear systems. Automatica 37, 857–869 (2001)
Sampaio, I.G.C.: Fault Tolerant Control of a Water Delivery Canal. Master Thesis. Instituto Superior Técnico (2012)
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Belfo, J.P., Lemos, J.M., Aguiar, A.P. (2021). Distributed LQ Control of a Water Delivery Canal Based on a Selfish Game. In: Gonçalves, J.A., Braz-César, M., Coelho, J.P. (eds) CONTROLO 2020. CONTROLO 2020. Lecture Notes in Electrical Engineering, vol 695. Springer, Cham. https://doi.org/10.1007/978-3-030-58653-9_45
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