Optimal Control of Elliptic Equations with Pointwise Constraints on the Gradient of the State in Nonsmooth Polygonal Domains

2012 ◽  
Vol 50 (4) ◽  
pp. 2117-2129 ◽  
Author(s):  
W. Wollner
Keyword(s):  
Optimal Control ◽  
Elliptic Equations ◽  
The State ◽  
Polygonal Domains ◽  
Pointwise Constraints

Error Estimates of Mixed Methods for Optimal Control Problems Governed by General Elliptic Equations

2016 ◽  
Vol 8 (6) ◽  
pp. 1050-1071 ◽  
Author(s):  
Tianliang Hou ◽  
Li Li
Keyword(s):  
Optimal Control ◽  
Finite Element ◽  
Error Estimates ◽  
Elliptic Equations ◽  
Optimal Control Problems ◽  
Mixed Finite Element ◽  
Control Variable ◽  
The State ◽  
Control Problems ◽  
General Elliptic

AbstractIn this paper, we investigate the error estimates of mixed finite element methods for optimal control problems governed by general elliptic equations. The state and co-state are approximated by the lowest order Raviart-Thomas mixed finite element spaces and the control variable is approximated by piecewise constant functions. We derive L2 and H–1-error estimates both for the control variable and the state variables. Finally, a numerical example is given to demonstrate the theoretical results.

scholarly journals Ana posteriorierror analysis for an optimal control problem with point sources

2018 ◽  
Vol 52 (5) ◽  
pp. 1617-1650 ◽  
Author(s):  
Alejandro Allendes ◽  
Enrique Otárola ◽  
Richard Rankin ◽  
Abner J. Salgado
Keyword(s):  
Optimal Control ◽  
Optimal Control Problem ◽  
Control Problem ◽  
Weighted Sobolev Spaces ◽  
Control Variable ◽  
The State ◽  
Point Sources ◽  
Adjoint Equations ◽  
Error Estimator ◽  
A Posteriori

We propose and analyze a reliable and efficienta posteriorierror estimator for a control-constrained linear-quadratic optimal control problem involving Dirac measures; the control variable corresponds to the amplitude of forces modeled as point sources. The proposeda posteriorierror estimator is defined as the sum of two contributions, which are associated with the state and adjoint equations. The estimator associated with the state equation is based on Muckenhoupt weighted Sobolev spaces, while the one associated with the adjoint is in the maximum norm and allows for unbounded right hand sides. The analysis is valid for two and three-dimensional domains. On the basis of the deviseda posteriorierror estimator, we design a simple adaptive strategy that yields optimal rates of convergence for the numerical examples that we perform.

STERILIZATION OF CANNED VISCOUS FOODS: AN OPTIMAL CONTROL APPROACH

2004 ◽  
Vol 14 (03) ◽  
pp. 355-374 ◽  
Author(s):  
L. J. ALVAREZ-VAZQUEZ ◽  
M. MARTA ◽  
A. MARTINEZ
Keyword(s):  
Optimal Control ◽  
Control Problem ◽  
Nutrient Retention ◽  
Reaction Diffusion ◽  
The State ◽  
Reaction Diffusion Equations ◽  
Boussinesq System ◽  
Temperature Dependent Viscosity ◽  
Control Approach ◽  
Dependent Viscosity

In this paper, we study an optimal control problem with pointwise constraints on state and control, related to sterilization processes involving heat transfer by natural convection. We introduce the mathematical model for the state system, which couples the Boussinesq system for temperature-dependent viscosity and the convection-reaction-diffusion equations, and we set the whole problem as a control problem, assuring the micro-organism reduction, the nutrient retention and the energy saving. The existence and the regularity of the state are studied. Finally, we obtain existence results for the optimal solutions and a first-order optimality condition for their characterization.

Optimal Control of a Model for a System Subject to Continuous Wear

1988 ◽  
Vol 2 (3) ◽  
pp. 321-328 ◽  
Author(s):  
Laurence A. Baxter ◽  
Eui Yong Lee
Keyword(s):  
Optimal Control ◽  
Brownian Motion ◽  
Poisson Process ◽  
Average Cost ◽  
Infinite Horizon ◽  
Arrival Rate ◽  
The State ◽  
Negative Drift ◽  
Random Amount

The state of a system is modelled by Brownian motion with negative drift and an absorbing barrier at the origin. A repairman arrives according to a Poisson process of rate λ. If the state of the system at arrival of the repairman does not exceed a certain threshold, he/she increases it by a random amount, otherwise no action is taken. Costs are assigned to each visit of the repairman, to each repair, and to the system being in state 0. It is shown that there exists a unique arrival rate λ which minimizes the average cost per unit time over an infinite horizon.

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