Trust-Region RB Methods for PDE-Constrained Optimization and Optimal Input Design

Andrea Petrocchi; Matthias K. Scharrer; Stefan Volkwein

Trust-Region RB Methods for PDE-Constrained Optimization and Optimal Input Design

Andrea Petrocchi^*, Matthias K. Scharrer, Stefan Volkwein

^*Corresponding author for this work

Virtual Vehicle Research GmbH (ViF) (98830)

Research output: Contribution to conference › Paper › peer-review

Abstract

In this paper we propose an algorithm for the bi-level optimal input design involving a parameter-dependent evolution problem. In the inner cycle a control is fixed and the parameter is optimized in order to minimize a cost function that measure the discrepancy from some data. In the outer cycle the found parameter is fixed and the control is now optimized in order to minimize a suitable measure of uncertainty of the parameters. The inner cycle uses a trustregion reduced basis approximation of the model with creation and enrichment of the reduced basis on-the-fly. Numerical examples illustrate the efficiency of the proposed approach.

Original language	English
Publication status	Published - 7 Sept 2022
Event	4th IFAC Workshop on Control of Systems Governed by Partial Differential Equations - Kiel, Germany Duration: 5 Sept 2022 → 7 Sept 2022 http://cpde2022.org/

Conference

Conference	4th IFAC Workshop on Control of Systems Governed by Partial Differential Equations
Abbreviated title	CPDE
Country/Territory	Germany
City	Kiel
Period	5/09/22 → 7/09/22
Internet address	http://cpde2022.org/

Cite this

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title = "Trust-Region RB Methods for PDE-Constrained Optimization and Optimal Input Design",

abstract = "In this paper we propose an algorithm for the bi-level optimal input design involving a parameter-dependent evolution problem. In the inner cycle a control is fixed and the parameter is optimized in order to minimize a cost function that measure the discrepancy from some data. In the outer cycle the found parameter is fixed and the control is now optimized in order to minimize a suitable measure of uncertainty of the parameters. The inner cycle uses a trustregion reduced basis approximation of the model with creation and enrichment of the reduced basis on-the-fly. Numerical examples illustrate the efficiency of the proposed approach.",

author = "Andrea Petrocchi and Scharrer, {Matthias K.} and Stefan Volkwein",

year = "2022",

month = sep,

day = "7",

language = "English",

note = "4th IFAC Workshop on Control of Systems Governed by Partial Differential Equations, CPDE ; Conference date: 05-09-2022 Through 07-09-2022",

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TY - CONF

T1 - Trust-Region RB Methods for PDE-Constrained Optimization and Optimal Input Design

AU - Petrocchi, Andrea

AU - Scharrer, Matthias K.

AU - Volkwein, Stefan

PY - 2022/9/7

Y1 - 2022/9/7

N2 - In this paper we propose an algorithm for the bi-level optimal input design involving a parameter-dependent evolution problem. In the inner cycle a control is fixed and the parameter is optimized in order to minimize a cost function that measure the discrepancy from some data. In the outer cycle the found parameter is fixed and the control is now optimized in order to minimize a suitable measure of uncertainty of the parameters. The inner cycle uses a trustregion reduced basis approximation of the model with creation and enrichment of the reduced basis on-the-fly. Numerical examples illustrate the efficiency of the proposed approach.

AB - In this paper we propose an algorithm for the bi-level optimal input design involving a parameter-dependent evolution problem. In the inner cycle a control is fixed and the parameter is optimized in order to minimize a cost function that measure the discrepancy from some data. In the outer cycle the found parameter is fixed and the control is now optimized in order to minimize a suitable measure of uncertainty of the parameters. The inner cycle uses a trustregion reduced basis approximation of the model with creation and enrichment of the reduced basis on-the-fly. Numerical examples illustrate the efficiency of the proposed approach.

M3 - Paper

T2 - 4th IFAC Workshop on Control of Systems Governed by Partial Differential Equations

Y2 - 5 September 2022 through 7 September 2022

ER -

Trust-Region RB Methods for PDE-Constrained Optimization and Optimal Input Design

Abstract

Conference

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