Stabilization of Steady Motions for Systems with Redundant Coordinates

Abstract

The vector-matrix Shulgin’s equations are used to stabilize the steady motions of mechanical systems with nonlinear geometric constraints in the case of incomplete information on the state. The momenta are introduced only for the cyclic coordinates that are not used to control. Three variants of the measurement vector are used to prove a theorem on the stabilization of control with the help of a part of the cyclic coordinates described by Lagrange variables. The control coefficients and the estimation system coefficients are specified by solving the corresponding Krasovskii linear-quadratic problem for a linear controlled subsystem without the critical variables corresponding to the redundant coordinates and to the introduced momenta. The stability of the complete closed nonlinear system is proved by reducing to a special Lyapunov case and by the application of the Malkin stability theorem in the case of time-varying perturbations.