Relative controllability of dynamic systems on linear approximation (Q2735899)

The problem of dynamic system controllability with respect to part of the variables is considered. The concept of a relative controllability is introduced and it is understood as a possibility of reaching points of a linear manifold by appropriate controls. For linear stationary systems theorems about a linear structure of the set of accessibility and a condition of accessibility of a linear manifold are obtained. Here, it is necessary to prove the theorem on local controllability of a nonlinear system with respect to a linear subspace by its linear approximation. NEWLINENEWLINENEWLINEAs an example, the controllability property of the gyrostat angular velocity by coupled gyrodyns (the two-phase gyroscopes) is studied. This mechanical system is uncontrollable because it has a first integral (integral of moment). The damping problem is of importance for control in many designs described by such models. The controllability of the carrier in a neighborhood of zero angular velocities is a corollary of the basic statement of the paper.