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Optimization Techniques for Data-Based Control and Machine Learning / von Katharina Bieker ; [Gutachter:innen Jun.-Prof. Dr. Sebastian Peitz, Prof. Dr. Sina Ober-Blöbaum, Prof. Dr. Stefan Klus]. Paderborn, 2023
Inhalt
Introduction
Theoretical Background
Optimal Control and Model Predictive Control
Optimal Control
Model Predictive Control
Data-Based Methods and Control
Data-Based Surrogate Modeling
The Basics of Machine Learning
Neural Networks
Data-Based Approximation of the Koopman Operator
Multiobjective Optimization
Pareto Optimality and Criticality
Solution Methods
DeepMPC for Flow Control - A Motivating Example
Design of the RNN
Application to a Fluid Flow Problem
Discussion
Utilizing Autonomous Models for Model Predictive Control
The Basic Idea of the QuaSiModO Framework
SUR for (Mixed) Integer Control Problems
Error Bounds
Numerical Experiments
Lorenz System & Koopman Operator:
Mackey-Glass Equation & ESN
Kármán Vortex Street & LSTM
Numerical Experiments on Data Efficiency
Treating l1-Regularized Problems via Multiobjective Continuation
The Continuation Method
Optimality Conditions for MOP-l1
Predictor
Corrector
Changing the Activation Structure
The Algorithm
Numerical Results
Toy Examples
SINDy
Neural Network
Towards High-Dimensional Problems
Generalization to Piecewise Differentiable Regularization Terms
The Structure of Pc
An Example - Support Vector Machines
Conclusion and Future Work
List of Abbreviations
Bibliography
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