On Applications of a new method for computing optimal non-linear feedback controls

A new method of computing optimal non-linear feedbacks is used for regulating the angular momentum of spacecraft using both reaction jets and flywheels. It is shown that the optimal feedback law satisfies a system of first-order, quasi-linear, partial differential equations. The integration of these equations by the method of characteristics gives the non-linear feedback control. This control reduces the angular velocities of the space vehicle to zero by minimizing the fuel consumption. The optimal regulation, under reaction jet control alone and with the flywheels at fixed angular velocities, is considered. The special case where these velocities are zero leads readily to the known analytical solution of the feedback law, which is linear in the state although the dynamics is non-linear.