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

210
views

0
downloads

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.
Finite bisimulations for switched linear systems Aydın Göl, Ebru; Lazar, Mircea; Belta, Calin (2013-02-04) In this paper, we consider the problem of constructing a finite bisimulation quotient for a discrete-time switched linear system in a bounded subset of its state space. Given a set of observations over polytopic subsets of the state space and a switched linear system with stable subsystems, the proposed algorithm generates the bisimulation quotient in a finite number of steps with the aid of sublevel sets of a polyhedral Lyapunov function. Starting from a sublevel set that includes the origin in its interio...
Finite Bisimulations for Switched Linear Systems Aydın Göl, Ebru; Lazar, Mircea; Belta, Calin (2014-12-01) In this paper, we consider the problem of constructing a finite bisimulation quotient for a discrete-time switched linear system in a bounded subset of its state space. Given a set of observations over polytopic subsets of the state space and a switched linear system with stable subsystems, the proposed algorithm generates the bisimulation quotient in a finite number of steps with the aid of sublevel sets of a polyhedral Lyapunov function. Starting from a sublevel set that includes the origin in its interio...
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...

Citation Formats

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.