Optimal Control of a Partially Known Coupled System of BOD and DO

Main Article Content

Laouar Chafia
Ayadi Abdelhamid
Hafdallah Abdelhak

Abstract

The work presented in this paper is concerned with the organic pollution problem and water quality valuation. Biochemical oxygen demand has been used to evaluate the quality of water. If organic matter is present the dissolved oxygen is consumed. This article considers an optimal control problem of coupled system with missing initial conditions, which presents the relation between the biochemical oxygen demand and the dissolved oxygen. The main objective is to control the concentration of dissolved oxygen using the information given in the biochemical oxygen demand equation. The main tool used to characterize the optimal control of the investigate system under the Pareto control formulation.

Article Details

References

  1. J. J. Mocuba, Dissolved oxygen and biochemical oxygen demand in the waters close to the Quelimane sewage discharge. MS Thesis. The University of Bergen (2010).
  2. J. Liu, G. Olsson, B. Mattiasson, Short-term BOD (BODst) as a parameter for on-line monitoring of biological treatment process, Biosensors Bioelectron. 20 (2004), 562–570.
  3. J. Liu, B. Mattiasson, Microbial BOD sensors for wastewater analysis, Water Res. 36 (2002), 3786–3802.
  4. J. L. Lions Contrˆole de Pareto de systemes distribues. Le cas stationnaire C. R. Acad. Sci. Paris S´er. I, 302 (6) (1986), 223-227.
  5. J. L. Lions, Control of Distributed Systems with incomplete Data. AMS Colloquium, Berkeley, 1983.
  6. J. L. Lions Controlea moindres regrets des systemes distribues. C. R. Acad. Sci. Paris Ser. I, 315(12) (1992), 1253–1257.
  7. J. L. Lions, No-regret and low-regret control, Environment, Economics and Their Mathematical Models, Masson, Paris, (1994).
  8. R. Dorville, O. Nakoulima, A. Omrane, On the control of ill-posed distributed parametersystems, ESAIM: Proc. 17 (2007), 50–66.
  9. R. Dorville, O. Nakoulima, A. Omrane, Controle optimal pour les problemes de controlabilite des systemes distribues a donnees manquantes, C. R. Math. Acad. Sci. Paris, Ser. I, 338(12) (2004), 921–924.
  10. O. Nakoulima, A. Omrane, J. Velin, No-regret control for nonlinear distributed systems with incomplete data, J. Math. Pures Appl. 81 (2002), 1161–1189.
  11. A. Hafdallah, A. Ayadi, Optimal control of a thermoelastic body with missing initial conditions, Int. J. Control. 93 (2020), 1570–1576.
  12. D. M. Reynolds, S. R. Ahmad, Rapid and direct determination of wastewater BOD values using a fluorescence technique, Water Res. 31 (1997), 2012–2018.
  13. J. Salguero, J. Valverde Flores, Reduction of the Biochemical Oxygen Demand of the water samples from the lower basin of the Chillon River by means of Air-Ozone MicroNanobubbles, Ventanilla - Callao, J. Nanotechnol. (Lima). 1 (2017), 25-35.
  14. M. Zajda, U. Aleksander-Kwaterczak, Wastewater Treatment Methods for Effluents from the Confectionery Industry – an Overview, J. Ecol. Eng. 20 (2019), 293–304.
  15. A. Hafdallah, A. Ayadi, C. Laouar, No-Regret Optimal Control Characterization for an Ill-Posed Wave Equation, Int. J. Math. Trends Techno. 41 (2017), 1-6.