Theoretical and Numerical Analysis of an Optimal Control Problem Related to Wastewater Treatment

2000 ◽  
Vol 38 (5) ◽  
pp. 1534-1553 ◽  
Author(s):  
A. Martínez ◽  
C. Rodríguez ◽  
M. E. Vázquez-Méndez
Keyword(s):  
Optimal Control ◽  
Wastewater Treatment ◽  
Numerical Analysis ◽  
Optimal Control Problem ◽  
Control Problem ◽  
Theoretical And Numerical Analysis

NUMERICAL ANALYSIS OF A MINIMAX OPTIMAL CONTROL PROBLEM WITH AN ADDITIVE FINAL COST

2002 ◽  
Vol 12 (02) ◽  
pp. 183-203 ◽  
Author(s):  
LAURA S. ARAGONE ◽  
SILVIA C. DI MARCO ◽  
ROBERTO L. V. GONZÁLEZ
Keyword(s):  
Optimal Control ◽  
Numerical Analysis ◽  
Optimal Control Problem ◽  
Convergence Rate ◽  
Control Problem ◽  
Discrete Solution ◽  
Discrete Scheme ◽  
Fully Discrete ◽  
Minimax Optimal Control ◽  
Continuous Problem

In this paper we deal with the numerical analysis of an optimal control problem of minimax type with finite horizon and final cost. To get numerical approximations we devise here a fully discrete scheme which enables us to compute an approximated solution. We prove that the fully discrete solution converges to the solution of the continuous problem and we also give the order of the convergence rate. Finally we present some numerical results.

scholarly journals Numerical Analysis of a Distributed Optimal Control Problem Governed by an Elliptic Variational Inequality

2015 ◽  
Vol 2015 ◽  
pp. 1-7
Author(s):  
Mariela Olguín ◽  
Domingo A. Tarzia
Keyword(s):  
Finite Element Method ◽  
Optimal Control ◽  
Finite Element ◽  
Variational Inequality ◽  
Numerical Analysis ◽  
Optimal Control Problem ◽  
Control Problem ◽  
State System ◽  
The Finite Element Method ◽  
Elliptic Variational Inequality

The objective of this work is to make the numerical analysis, through the finite element method with Lagrange’s triangles of type 1, of a continuous optimal control problem governed by an elliptic variational inequality where the control variable is the internal energyg. The existence and uniqueness of this continuous optimal control problem and its associated state system were proved previously. In this paper, we discretize the elliptic variational inequality which defines the state system and the corresponding cost functional, and we prove that there exist a discrete optimal control and its associated discrete state system for each positiveh(the parameter of the finite element method approximation). Finally, we show that the discrete optimal control and its associated state system converge to the continuous optimal control and its associated state system when the parameterhgoes to zero.

scholarly journals An optimal control problem applied to a wastewater treatment plant

2021 ◽  
Vol 0 (0) ◽  
pp. 0
Author(s):  
M. Teresa T. Monteiro ◽  
Isabel Espírito Santo ◽  
Helena Sofia Rodrigues
Keyword(s):  
Mathematical Model ◽  
Optimal Control ◽  
Wastewater Treatment ◽  
Optimal Control Problem ◽  
Dissolved Oxygen ◽  
Activated Sludge ◽  
Control Problem ◽  
Control Variable ◽  
Treatment Plant ◽  
Domestic Effluent

<p style='text-indent:20px;'>This paper aims to present a mathematical model that describes the operation of an activated sludge system during one day. Such system is used in the majority of wastewater treatment plants and depends strongly on the dissolved oxygen, since it is a biological treatment. To guarantee the appropriate amount of dissolved oxygen, expensive aeration strategies are demanded, leading to high costs in terms of energy consumption. It was considered a typical domestic effluent as the wastewater to test the mathematical model and it was used the ASM1 to describe the activated sludge behaviour. An optimal control problem was formulated whose cost functional considers the trade-off between the minimization of the control variable herein considered (the dissolved oxygen) and the quality index that is the amount of pollution. The optimal control problem is treated as a nonlinear optimization problem after discretization by direct methods. The problem was then coded in the AMPL programming language in order to carry out numerical simulations using the NLP solver IPOPT from NEOS Server.</p>

REDUCED MODEL OF PLASMA DISCHARGE CONTROL IN TOKAMAK WITH IRON CORE

2020 ◽  
Vol 7 (3) ◽  
pp. 11-22
Author(s):  
VALERY ANDREEV ◽  
◽  
ALEXANDER POPOV
Keyword(s):  
Optimal Control ◽  
Inverse Problem ◽  
Optimal Control Problem ◽  
Control Problem ◽  
Nonlinear Behavior ◽  
Plasma Discharge ◽  
Reduced Model ◽  
Iron Core ◽  
Power Sources ◽  
Real Power

A reduced model has been developed to describe the time evolution of a discharge in an iron core tokamak, taking into account the nonlinear behavior of the ferromagnetic during the discharge. The calculation of the discharge scenario and program regime in the tokamak is formulated as an inverse problem - the optimal control problem. The methods for solving the problem are compared and the analysis of the correctness and stability of the control problem is carried out. A model of “quasi-optimal” control is proposed, which allows one to take into account real power sources. The discharge scenarios are calculated for the T-15 tokamak with an iron core.

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