On Generalized Homogenezation of Linear Controllers

Homogeneity is a dilation symmetry, which can be discovered for functions and vector fields in finite dimensional Euclidean spaces as well as for functionals and operators in infinite dimensional Banach and Hilbert spaces. Many models of mathematical physics are homogeneous in a generalized sense. This talk presents a brief introduction to the so-called generalized homogeneous control systems as well as a possible way to use the generalized homogeneity for an "upgrade" of linear (e.g. PID) controllers. Theoretical results are supported by real experiments with the quadrotor QDrone of Quanser.