The recent developments in the research area indicate a significant shift towards leveraging advanced mathematical frameworks and innovative computational techniques to address complex problems across various domains. A notable trend is the extension of traditional methods, such as the Kaczmarz algorithm, to tensor systems, enabling more efficient and accurate solutions for high-dimensional data problems like image deblurring. Additionally, there is a growing emphasis on adaptive and robust identification algorithms, particularly those that can handle saturated observations and non-traditional system signals, which are crucial for applications in fields such as judicial sentencing prediction. Optimal control problems, constrained by complex kinetic equations, are being tackled using novel hypocoercivity frameworks, ensuring stability and robustness in the solutions. The field is also witnessing advancements in low-rank matrix factorization and robust PCA, with new models integrating adaptive weighted least squares to enhance performance and stability. Neural adaptive spectral methods are emerging as powerful tools for solving optimal control problems efficiently, offering substantial speedups and high generalization capabilities. Furthermore, the application of optimal transport theory to ensemble control problems provides new insights and computational efficiencies, particularly in state tracking scenarios with limited observations. Overall, the research is progressing towards more flexible, adaptive, and robust solutions that can handle a wider range of complex systems and data structures.