On minimal and on excessive sets of transverse coordinates for controlling a motion of a nonlinear mechanical system

Abstract:
The talk is aimed at discussion of different analytic and computational formats of transverse coordinates suggested for characterizing the so-called transverse dynamics in a vicinity of forced motion of controlled mechanical system. The contribution complements the classical results of Leonov, Zubov, Demidovich, Andronov if such coordinates are chosen for deriving the linearization of the transverse dynamics and analysis of orbital or Zhukovsky stability of motion by first approximation. Meanwhile, the new characterization of the transverse dynamics goes beyond and allows new tools for developing feedback controllers for orbital stabilization of the forced motion of highly nonlinear and underactuated mechanical systems. The contribution is illustrated by several examples.