Minimum-Time Optimal Control for a Model of Biological Wastewater Treatment

We consider a mathematical model that describes biological treatment of wastewater. The model is a controlled nonlinear three-dimensional system of differential equations. A minimum-time optimal control problem is posed that achieves the required contaminant concentration in the shortest possible time. The problem is investigated by Pontryagin’s maximum principle. The optimal control in this problem is represented by a switching function and its properties are analyzed. The results of this analysis make it possible to reduce the solution of the problem to a successive application of finite-dimensional constrained minimization and the parameter continuation method. The application of these approaches is discussed in detail, and the relevant numerical results are reported.

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Correspondence to E. V. Grigor’eva.

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Grigor’eva, E.V., Khailov, E.N. Minimum-Time Optimal Control for a Model of Biological Wastewater Treatment. Comput Math Model 31, 179–189 (2020). https://doi.org/10.1007/s10598-020-09487-7

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Keywords

  • biological wastewater treatment
  • minimum-time optimal control
  • mathematical model
  • Pontryagin’s maximum principle