Multivariable Control: Weighting Matrices and Gaussian Random Vectors

This lecture covers the design of weighting matrices for the LQR method, focusing on the selection criteria and the trial-and-error process involved. It also delves into the concept of Gaussian random vectors, discussing their properties, mean, variance, and the implications of different covariance structures. The instructor explains the modal analysis of systems with distinct eigenvalues, emphasizing the importance of selecting specific modes for control. Additionally, the lecture explores the normalization approach for choosing weights in the LQR problem, addressing the issue of scale-dependency and providing a method to handle variables measured in different units.