Open MSc thesis positions:
1. Leveraging repetitive and iterative learning control for identifying nonlinear modes.
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Nonlinear vibration modes are exciting concepts from nonlinear systems theory that are merely defined as periodic oscillations but that may exhibit complex behaviours. As is the case for linear systems, these vibration modes are features mechanical engineers like to manipulate when it comes to analysing, designing and controlling nonlinear systems. However, experimentally identifying nonlinear modes still stands as a significant scientific challenge. In this research, we follow an unconventional research path in the field by exploiting recent advances in repetitive and iterative learning control towards performing nonlinear mode identification.

2. Nonlinear mechanical systems = Dynamic networks?
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This research explores the equivalences and dissimilarities between nonlinear mechanical system equations and dynamic network representations. Our overall objective is the development of a data-driven topology detection methodology, applicable to nonlinear mechanics, but that operates in a network setting. This research finds highly relevant applications in situations where unwanted nonlinearities are suspected to hinder the optimal performance of complex systems.

3. How to model friction in mechatronics? A machine learning answer.
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Friction is arguably one the most complex kinds of nonlinearities to model in mechanics. It also appears to ever more significantly affect the dynamics of most mechatronic systems, posing a serious challenge to linear model-based control techniques. This project adopts a machine learning philosophy to develop accurate and versatile models of friction dynamics. Different strategies are investigated, with a special focus put onto wrapper approaches, where measurement data are augmented with model-simulations to train powerful nonlinear mappings like deep neural networks and regression trees.

4. Model uncertainty and control robustness in the presence of nonlinearities: a statistics challenge.
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Quantifying uncertainties is, for a long time, perceived as an integral part of the data-driven modelling process, especially because it naturally supports robust control purposes. In the presence of modelling errors, that are inherent to nonlinear dynamic system representations, the actual variability of the model parameters is however known to be (sometimes markedly) underestimated. This project leverages the random matrix theory to analyse uncertainties in nonlinear data-driven models. Intrinsically, we transform a bias-related problem, i.e. the presence of modelling errors, into a variance problem, i.e. the calculation of uncertainty bounds, by fully randomising the parameter matrix elements in nonlinear state-space models. The added value of this research is also investigated in the context of the robust control of nonlinear dynamic systems.

5. What does my nonlinear data-driven model mean? Let's inspect its bifurcations.
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A nonlinear data-driven model is typically seen as an aggregate of parameters, from which interpretation can occasionally be retrieved. In this project, we put forward the idea of regarding such a model of as means of conveying intrinsic system dynamic features. In particular, it is proposed to develop a general numerical algorithm that calculates bifurcations from nonlinear data-driven models and, in doing so, that reveals their key physical meaning. Quantifying uncertainties on the bifurcation properties caused by modelling imperfections is also within the scope of this project.

6. Model-based vs. model-free data-driven linearisation of nonlinear dynamic systems.
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Currently active MSc student on this subject: Merijn Floren.

7. Physics-based vs. data-based modelling in thermal control problems.
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Currently active MSc student on this subject: Raoul Surie.