Lukas Ecker,
"Contributions to the Combination of Model-Based and Data-Driven Techniques in Control Theory"
, 2-2024
Original Titel:
Contributions to the Combination of Model-Based and Data-Driven Techniques in Control Theory
Sprache des Titels:
Englisch
Original Kurzfassung:
This thesis focuses on integrating data-based methods into the model-based observer and controller design for nonlinear dynamical systems. Classical model-based design methods involve mathematical models to determine stabilizing control laws or observer systems. These models can often be derived from fundamental physical, chemical, or biological laws in natural sciences. The governing equations allow the simulation and prediction of the system?s future behavior. Model-based observer and controller design approaches utilize various techniques from different areas of mathematics, such as functional analysis, differential geometry, or optimization. Challenging real-world problems can be solved using advanced mathematical design methods from nonlinear control theory. However, model-based methods are often susceptible to modeling inaccuracies. These methods necessitate intricate model identification and validation processes, which can be particularly demanding. In addition, the mathematical tools for deriving the controller and observer can become very complex.
On the other hand, data-based methods rely primarily on recorded data sets to design control or observation strategies. They are beneficial when the system behavior is highly complex, and creating an exact mathematical model would involve considerable difficulty and effort. However, the quality and quantity of the available data sets significantly influence the quality of the designed data-based controller or observer. As the methods mentioned are usually only based on empirical observations of the system behavior, mathematically exact stability statements are often impossible. Comparing purely data-based and purely model-based design methods depends on various factors, including the availability of data, the accuracy of the model, robustness to changes in system behavior, and computational complexity. Combining data- and model-based methods is a promising approach that aims to combine the advantages of both concepts. This cumulative work is dedicated to precisely this topic. It comprises several contributions to the combined data- and model-based design systematics. The focus is on the question of how data-based approaches from the fields of stochastics and machine learning can be favorably integrated into classical design approaches. Essentially,
three specific problem areas are addressed. Firstly, attempts are made to improve the computational efficiency of model-based algorithms such as the Bayesian state observer. For this purpose, stochastic processes and machine learning methods are combined with the analytically derived propagation and inference steps of the observer. Compared to
conventional particle filter algorithms, the computational effort can be reduced while maintaining at least the same observer accuracy. The second topic covered is the integration of data-based methods in scenarios with very complex system dynamics. The main focus here is on the data-based modeling and the indirect data-driven observer design for nonlinear switched systems. The aim is to avoid the often time-consuming and costly
mathematical modeling using supervised and unsupervised machine learning techniques. Finally, the integration of data-based techniques into the controller and observer design with canonical normal forms is investigated. Here, the idea is to learn necessary transformations into canonical system representations using elements of artificial intelligence, such as neural networks and autoencoder structures. In this way, advanced controller and observer design methods can be derived on the basis of a Brunovsky structure without the need for a mathematically sophisticated analytical derivation of the necessary system
transformations.
Forschungs-