Optimal control of a rotational motion of a gyrostat on circular orbit

A control scheme is proposed to guarantee an optimal stabilization of a given rotational motion of a symmetric gyrostat on circular orbit. The gyrostat controlled by the control action generated by rotating internal rotors. In such study the asymptotic stability of this motion is proved using Barbachen and Krasovskii theorem's and the optimal control law is deduced from the conditions that ensure the optimal asymptotic stability of the desired motion. As a particular case, the equilibrium position of the gyrostat, which occurs when the principal axes of inertia coincide with the orbital axes, is proved to be asymptotically stable. The present method is shown to more general than previous ones.