POD-Based Economic Optimal Control of Heat-Convection Phenomena

Mechelli, Luca; Volkwein, Stefan

POD-Based Economic Optimal Control of Heat-Convection Phenomena

Files

Mechelli_2--au6ei3apyzpv0.pdf(746.28 KB)

Date

2017

Authors

Mechelli, Luca

Volkwein, Stefan

Series

Konstanzer Schriften in Mathematik; 365

Publication type

Working Paper/Technical Report

Publication status

Published

Abstract

In the setting of energy efficient building operation, an optimal boundary control problem governed by the heat equation with a convection term is considered together with bilateral control and state constraints. The aim is to keep the tem- perature in a prescribed range with the less possible heating cost. In order to gain regular Lagrange multipliers a Lavrentiev regularization for the state constraints is utilized. The regularized optimal control problem is solved by a primal-dual active set strategy (PDASS) which can be interpreted as a semismooth Newton method and, therefore, has a superlinear rate of convergence. To speed up the PDASS a reduced-order approach based on proper orthogonal decomposition (POD) is ap- plied. An a-posterori error analysis ensures that the computed (suboptimal) POD solutions are sufficiently accurate. Numerical test illustates the efficiency of the pro- posed strategy.

Subject (DDC)

510 Mathematics

Cite This

ISO 690

MECHELLI, Luca, Stefan VOLKWEIN, 2017. POD-Based Economic Optimal Control of Heat-Convection Phenomena

BibTex

@techreport{Mechelli2017PODBa-40437,
  year={2017},
  series={Konstanzer Schriften in Mathematik},
  title={POD-Based Economic Optimal Control of Heat-Convection Phenomena},
  number={365},
  author={Mechelli, Luca and Volkwein, Stefan}
}

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