Hybrid Magnetic Attitude Control of Spacecraft: Optimality, Passivity, and Stability

Hybrid spacecraft attitude control schemes that combine magnetic torques with impulsive thrusting in an optimal or passive manner are developed. The optimal controller uses a hybrid linear quadratic regulator formulation, while explicitly accounting for a priori estimates of the disturbances. Previous results on optimal impulse timing are extended to remain valid under disturbance accommodation, and the special case of a multi-orbit mission with repeating impulse patterns is considered. The passivity-based approach relies on a hybrid and time-varying extension of Kalman-Yakubovich-Popov conditions, and judiciously designs the output dynamics to guarantee passivity of the plant and stability of the closed-loop system subject to sufficiently small disturbances. Lastly, input/output stability of the disturbance-accommodating controller and Lyapunov stability of the passive controller are studied by introducing a hybrid state transition matrix. Extensions of the classical Floquet theory and its counterpart for inhomogeneous systems provide stability analysis tools for the proposed hybrid controllers.M.A.S