Kinematic Problem of Optimal Nonlinear Stabilization of Angular Motion of a Rigid Body

The problem of optimal transfer of a rigid body to a prescribed trajectory of preset angular motion is considered in the nonlinear statement. (The control is the vector of absolute angular velocity of the rigid body.) The functional to be minimized is a mixed integral quadratic performance criterion characterizing the general energy expenditure on the control and deviations in the state coordinates. Pontryagin's maximum principle is used to construct the general analytic solution of the problem in question which satisfies the necessary optimality condition and ensures the asymptotically stable transfer of the rigid body to any chosen trajectory of preset angular motion. It is shown that the obtained solution also satisfies Krasovskii's optimal stabilization theorem.