Show/Hide Menu
Hide/Show Apps
Logout
Türkçe
Türkçe
Search
Search
Login
Login
OpenMETU
OpenMETU
About
About
Open Science Policy
Open Science Policy
Communities & Collections
Communities & Collections
Help
Help
Frequently Asked Questions
Frequently Asked Questions
Guides
Guides
Thesis submission
Thesis submission
MS without thesis term project submission
MS without thesis term project submission
Publication submission with DOI
Publication submission with DOI
Publication submission
Publication submission
Supporting Information
Supporting Information
General Information
General Information
Copyright, Embargo and License
Copyright, Embargo and License
Contact us
Contact us
Local improvements to reduced-order approximations of optimal control problems governed by diffusion-convection-reaction equation
Date
2015-07-01
Author
Akman, Tuğba
Metadata
Show full item record
This work is licensed under a
Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License
.
Item Usage Stats
71
views
0
downloads
Cite This
We consider the optimal control problem governed by diffusion-convection-reaction equation without control constraints. The proper orthogonal decomposition (POD) method is used to reduce the dimension of the problem. The POD method may lack accuracy if the POD basis depending on a set of parameters is used to approximate the problem depending on a different set of parameters. To increase the accuracy and the robustness of the basis, we compute five bases additional to the baseline POD in case of the perturbation of the diffusion term, a parameter in the convection field, the reaction term and Tikhonov regularization term. For the first two bases, we use the sensitivity information to extrapolate and expand the baseline POD basis. The other one is based on the subspace angle interpolation method. Multiple snapshot sets are used to derive the last two bases. A-posteriori error estimator is used to analyse the difference between the suboptimal control, computed using the POD basis, and the optimal control. We compare these different bases in terms of accuracy and complexity, investigate the advantages and main drawbacks of them.
Subject Keywords
Optimal control problem
,
Proper orthogonal decomposition
,
Sensitivity analysis
,
Subspace angle interpolation method
,
POD-Greedy method
,
A-posteriori error estimates
URI
https://hdl.handle.net/11511/62294
Journal
COMPUTERS & MATHEMATICS WITH APPLICATIONS
DOI
https://doi.org/10.1016/j.camwa.2015.04.017
Collections
Department of Mathematics, Article
Suggestions
OpenMETU
Core
Distributed optimal control of time-dependent diffusion-convection-reaction equations using space-time discretization
Seymen, Z. Kanar; Yücel, Hamdullah; Karasözen, Bülent (2014-05-01)
We apply two different strategies for solving unsteady distributed optimal control problems governed by diffusion-convection-reaction equations. In the first approach, the optimality system is transformed into a biharmonic equation in the space time domain. The system is then discretized in space and time simultaneously and solved by an equation-based finite element package, i.e., COMSOL Multiphysics. The second approach is a classical gradient-based optimization method to solve the state and adjoint equati...
Distributed Optimal Control Problems Governed by Coupled Convection Dominated PDEs with Control Constraints
Yücel, Hamdullah (2013-08-30)
We study the numerical solution of control constrained optimal control problems governed by a system of convection diffusion equations with nonlinear reaction terms, arising from chemical processes. Control constraints are handled by using the primal-dual active set algorithm as a semi-smooth Newton method or by adding a Moreau-Yosida-type penalty function to the cost functional. An adaptive mesh refinement indicated by a posteriori error estimates is applied for both approaches.
Variational time discretization methods for optimal control problems governed by diffusion-convection-reaction equations
Akman, Tugba; Karasözen, Bülent (2014-12-15)
In this paper, the distributed optimal control problem governed by unsteady diffusion-convection-reaction equation without control constraints is studied. Time discretization is performed by variational discretization using continuous and discontinuous Galerkin methods, while symmetric interior penalty Galerkin with upwinding is used for space discretization. We investigate the commutativity properties of the optimize-then-discretize and discretize-then-optimize approaches for the continuous and discontinuo...
Model order reduction for nonlinear Schrodinger equation
Karasözen, Bülent; Uzunca, Murat (2015-05-01)
We apply the proper orthogonal decomposition (POD) to the nonlinear Schrodinger (NLS) equation to derive a reduced order model. The NLS equation is discretized in space by finite differences and is solved in time by structure preserving symplectic mid-point rule. A priori error estimates are derived for the POD reduced dynamical system. Numerical results for one and two dimensional NLS equations, coupled NLS equation with soliton solutions show that the low-dimensional approximations obtained by POD reprodu...
Dynamic programming for a Markov-switching jump-diffusion
Azevedo, N.; Pinheiro, D.; Weber, Gerhard Wilhelm (Elsevier BV, 2014-09-01)
We consider an optimal control problem with a deterministic finite horizon and state variable dynamics given by a Markov-switching jump-diffusion stochastic differential equation. Our main results extend the dynamic programming technique to this larger family of stochastic optimal control problems. More specifically, we provide a detailed proof of Bellman's optimality principle (or dynamic programming principle) and obtain the corresponding Hamilton-Jacobi-Belman equation, which turns out to be a partial in...
Citation Formats
IEEE
ACM
APA
CHICAGO
MLA
BibTeX
T. Akman, “Local improvements to reduced-order approximations of optimal control problems governed by diffusion-convection-reaction equation,”
COMPUTERS & MATHEMATICS WITH APPLICATIONS
, pp. 104–131, 2015, Accessed: 00, 2020. [Online]. Available: https://hdl.handle.net/11511/62294.