This thesis explores the development and application of clustering-based reduced-order modeling (ROM) for chaotic systems, with an emphasis on both predictive modeling and control strategies. Chaotic systems, characterized by their sensitivity to initial conditions and complex spatio-temporal dynamics, present significant challenges in terms of prediction and control. Traditional numerical methods for solving these systems are computationally intensive and often impractical for real-time applications. Reduced-order modeling techniques, which seek to represent high-dimensional systems in lower-dimensional subspaces, offer a promising alternative.

Clustering-based ROM is highlighted as a potentially effective method due to its data-driven nature and computational efficiency. This study focuses on studying the influence of different parameters in the clustering-based ROM approach in modeling and developing a robust control algorithm to mitigate extreme events. This is investigated on three different chaotic systems of increasing complexity: the Lorenz system, the truncated Charney-DeVore (CDV) system and the Moehlis-Faisst-Eckhart (MFE) system. The ability of the clustering-based ROM in reproducing those systems' statistics is confirmed. The influence of the number of clusters and the order of modeling on the ROM accuracy is explored, and a quantitative method to determine the number of clusters when modeling with clustering-based ROM is proposed.

For the control part, a clustering-based control strategy is applied to the CDV system and MFE system. In the CDV system, the control aims to move the system away from the blocked state, and in the MFE system, the objective is to prevent extreme events (which take the form of quasi-relaminarisation events). In both cases, the clustering-based control manages to achieve these objectives, with a reduction of 90% of extreme events in the MFE case. These results highlight the potential of clustering-based control.

This research contributes to the field by providing a viable approach to managing chaotic systems with reduced computational demands, offering potential applications in various engineering and scientific domains.