Optimal management of a two dam system via stochastic control: parallel computing approach

Boris Miller; Daniel McInnes

doi:10.1109/CDC.2011.6160566

Optimal management of a two dam system via stochastic control: parallel computing approach

Boris Miller, Daniel McInnes

School of Mathematics

Research output: Chapter in Book/Report/Conference proceeding › Conference Paper › Research › peer-review

12 Citations (Scopus)

Abstract

In this paper we consider a model for the optimal management of a two dam system. Each dam is modelled via a continuous-time controlled Markov chain on a finite control period and linked to the other dam via a state and time dependent water transfer control. The consumption control for the dam system is provided by a time and state dependent price feedback control. This price feedback control takes into account the active seasonal demands of customers. We consider the case where inflow processes and evaporation for each dam are non-stationary as are the customer demands. The general approach to the solution of this problem is to consider this stochastic optimisation problem in the average case and solve it using the dynamic programming method. We show that the use of parallel computing techniques leads to substantial savings in calculation times for the solution of the optimal controls and demonstrate this via a numerical example.

Original language	English
Title of host publication	Proceedings of the 50th IEEE Conference on Decision and Control and European Control Conference (CDC-ECC)
Editors	Marios Polycarpou
Place of Publication	USA
Publisher	IEEE, Institute of Electrical and Electronics Engineers
Pages	1417 - 1423
Number of pages	7
DOIs	https://doi.org/10.1109/CDC.2011.6160566
Publication status	Published - 2011
Event	IEEE Conference of Decision and Control (CDC)/European Control Conference (ECC) 2011 - Hilton Orlando Bonnet Creek, Orlando, United States of America Duration: 12 Dec 2011 → 15 Dec 2011 Conference number: 50th http://www.ieeecss.org/CAB/conferences/cdcecc2011/cfp.php https://www.ieee.org/conferences_events/conferences/conferencedetails/index.html?Conf_ID=15803

Conference

Conference	IEEE Conference of Decision and Control (CDC)/European Control Conference (ECC) 2011
Abbreviated title	CDC-ECC 2011
Country/Territory	United States of America
City	Orlando
Period	12/12/11 → 15/12/11
Other	2011 50th IEEE Conference on Decision and Control and European Control Conference, CDC-ECC 2011
Internet address	http://www.ieeecss.org/CAB/conferences/cdcecc2011/cfp.php https://www.ieee.org/conferences_events/conferences/conferencedetails/index.html?Conf_ID=15803

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Miller, B., & McInnes, D. (2011). Optimal management of a two dam system via stochastic control: parallel computing approach. In M. Polycarpou (Ed.), Proceedings of the 50th IEEE Conference on Decision and Control and European Control Conference (CDC-ECC) (pp. 1417 - 1423). IEEE, Institute of Electrical and Electronics Engineers. https://doi.org/10.1109/CDC.2011.6160566

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abstract = "In this paper we consider a model for the optimal management of a two dam system. Each dam is modelled via a continuous-time controlled Markov chain on a finite control period and linked to the other dam via a state and time dependent water transfer control. The consumption control for the dam system is provided by a time and state dependent price feedback control. This price feedback control takes into account the active seasonal demands of customers. We consider the case where inflow processes and evaporation for each dam are non-stationary as are the customer demands. The general approach to the solution of this problem is to consider this stochastic optimisation problem in the average case and solve it using the dynamic programming method. We show that the use of parallel computing techniques leads to substantial savings in calculation times for the solution of the optimal controls and demonstrate this via a numerical example.",

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publisher = "IEEE, Institute of Electrical and Electronics Engineers",

address = "United States of America",

note = "IEEE Conference of Decision and Control (CDC)/European Control Conference (ECC) 2011, CDC-ECC 2011 ; Conference date: 12-12-2011 Through 15-12-2011",

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Miller, B & McInnes, D 2011, Optimal management of a two dam system via stochastic control: parallel computing approach. in M Polycarpou (ed.), Proceedings of the 50th IEEE Conference on Decision and Control and European Control Conference (CDC-ECC). IEEE, Institute of Electrical and Electronics Engineers, USA, pp. 1417 - 1423, IEEE Conference of Decision and Control (CDC)/European Control Conference (ECC) 2011, Orlando, Florida, United States of America, 12/12/11. https://doi.org/10.1109/CDC.2011.6160566

Optimal management of a two dam system via stochastic control: parallel computing approach. / Miller, Boris; McInnes, Daniel.
Proceedings of the 50th IEEE Conference on Decision and Control and European Control Conference (CDC-ECC). ed. / Marios Polycarpou. USA: IEEE, Institute of Electrical and Electronics Engineers, 2011. p. 1417 - 1423.

Research output: Chapter in Book/Report/Conference proceeding › Conference Paper › Research › peer-review

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N2 - In this paper we consider a model for the optimal management of a two dam system. Each dam is modelled via a continuous-time controlled Markov chain on a finite control period and linked to the other dam via a state and time dependent water transfer control. The consumption control for the dam system is provided by a time and state dependent price feedback control. This price feedback control takes into account the active seasonal demands of customers. We consider the case where inflow processes and evaporation for each dam are non-stationary as are the customer demands. The general approach to the solution of this problem is to consider this stochastic optimisation problem in the average case and solve it using the dynamic programming method. We show that the use of parallel computing techniques leads to substantial savings in calculation times for the solution of the optimal controls and demonstrate this via a numerical example.

AB - In this paper we consider a model for the optimal management of a two dam system. Each dam is modelled via a continuous-time controlled Markov chain on a finite control period and linked to the other dam via a state and time dependent water transfer control. The consumption control for the dam system is provided by a time and state dependent price feedback control. This price feedback control takes into account the active seasonal demands of customers. We consider the case where inflow processes and evaporation for each dam are non-stationary as are the customer demands. The general approach to the solution of this problem is to consider this stochastic optimisation problem in the average case and solve it using the dynamic programming method. We show that the use of parallel computing techniques leads to substantial savings in calculation times for the solution of the optimal controls and demonstrate this via a numerical example.

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Optimal management of a two dam system via stochastic control: parallel computing approach

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