Chaos and optimal control of steady-state rotation of a satellite-gyrostat on a circular orbit

The present paper is devoted to discuss both the chaos and optimal control of the steady rotations of a satellite-gyrostat on a circular orbit. In this the satellite is controlled with the help of three independent control moments that are developed by three rotors attached to the satellite principal axes of inertia and rotate with the help of motors rigidly mounted on the satellite body. The optimal controllers that asymptotically stabilize these chaotic rotations and minimize the required like-energy cost are derived as a function of the phase coordinates of the system. The asymptotic stability of the resulting nonlinear system is proved using the Liapunov technique. Numerical study and examples are introduced.