Stabilization of the programmed motions of a rigid body with uncertainty in the parameters of the equations of dynamics

A control scheme is proposed to guarantee the asymptotic stability of a given programmed motion of a rigid body rotating about a fixed point. The body is controlled by means of a couple of reactive forces, or the control action is created by rotating flywheels. The inertial parameters and angular momentum of the system rue estimated while the motion is in progress. The control is synthesized by expressing the equations of dynamics in a form that is linear in the parameter vector and by using the passivity property of the dynamical object. A law is proposed for the control and for adjusting the parameters that guarantees the asymptotic stability of the motion and, for programmed motions that satisfy the condition of non-vanishing action, guarantees the convergence of the vector of adjusted parameters to its true value. The domain in phase space for which exponential stabilization is achieved is determined. (C) 1997 Elsevier Science Ltd. All rights reserved.