Data-Driven Model-Order Reduction for Model Predictive Control

Rohleff, Jan

Data-Driven Model-Order Reduction for Model Predictive Control

Dateien

Rohleff_2-1mu5q5d2uids85.pdfGröße: 4.25 MBDownloads: 154

Datum

2023

Open Access-Veröffentlichung

Open Access Green

Sammlungen

Mathematik und Statistik

Publikationstyp

Masterarbeit/Diplomarbeit

Publikationsstatus

Published

Zusammenfassung

In this thesis, quadratic optimal control problems for linear parabolic partial differen- tial equations (PDEs) with time-dependent coefficient functions are considered. After showing the existence and uniqueness of the solution, necessary and sufficient first order optimality conditions are derived. By applying a finite element (FE) discretization, the first-order optimality system can be represented as a linear time-variant (LTV) coupled dynamical system, which encompasses both the state equation and the dual equation. This leads us into the area of dynamical systems. Model predictive control (MPC) is applied to solve the problem over the long-time horizon. To speedup the computational time three data-driven model-order reduction (MOR) techniques are applied: Proper or- thogonal decomposition (POD), empirical gramians and extended dynamic mode decom- position (EDMD). Furthermore, an a-posteriori error analysis is conducted to guarantee the accuracy of the reduced model during the MPC. Numerical simulations illustrate the advantages and disadvantages of the various MOR techniques.

Fachgebiet (DDC)

510 Mathematik

Schlagwörter

Dynamical Systems, Optimal Control, Model-Order Reduction, Model Predictive Control, Empirical Gramians, Proper Orthogonal Decomposition, Extended Dynamic Mode Decomposition, POD, EDMD, Time-Variant Systems, Semismooth Newton

Zitieren

ISO 690

ROHLEFF, Jan, 2023. Data-Driven Model-Order Reduction for Model Predictive Control [Master thesis]. Konstanz: Universität Konstanz

BibTex

@mastersthesis{Rohleff2023DataD-66556,
  year={2023},
  title={Data-Driven Model-Order Reduction for Model Predictive Control},
  address={Konstanz},
  school={Universität Konstanz},
  author={Rohleff, Jan}
}

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Hochschulschriftenvermerk

Konstanz, Universität Konstanz, Masterarbeit/Diplomarbeit, 2023

Universitätsbibliographie

Ja