Optimal stabilization of an equilibrium position of a rigid body using rotors system with friction forces

The optimal stabilization of one class of equilibrium positions of a rigid body using rotors system with internal friction is studied. The performance index is an integral form of a quadratic function in the state and control variables. Both of the angular velocity and orientation variables are regulated. The optimal driving control moments which stabilize this position are obtained using the conditions of ensuring the optimal asymptotic stability of this position as non-linear functions of phase coordinates of the body. Some known results on the optimal control of equilibrium positions of a rigid body are improved and new results are obtained. Numerical simulation is presented.