This dissertation investigates the nonlinear control of the attitude for an underactuated rigid-body spacecraft system in the body-orbital and inertial frames. The problem involving the stabilization of the body-orbital attitude of an underactuated output-feedback system is examined. Using sliding mode control in conjunction with finite-time nonlinear observer, a novel observer-based control law is rigorously analyzed and proven to achieve attitude convergence. Under time-varying disturbances, inertia matrix uncertainties, and high initial errors, the proposed novel law achieves attitude convergence for three-axis stability and ultimate boundedness within 5 degrees and 0.01 deg/s, for attitude error norm and angular velocity norm, respectively. Next, the attitude control problem is rigorously analyzed in the inertial frame, where the underactuated rigid-body spacecraft system equations of motion are highly nonlinear, and the linearized equations of motion are not controllable. To this end, a generalized velocity-free time-varying state feedback controller is developed to achieve globally exponential stability with respect to the homogenous norm and proven to provide ultimate boundedness of all signals with 5 degrees attitude error norm and 0.5 rad/s angular velocity error norm. Finally, the inertial frame attitude stabilization problem is treated as an optimal control problem. For this case, the Legendre pseudospectral method is used to discretized the spacecraft dynamics into Legendre-Gauss-Lobatto (LGL) node points, where the Lagrange polynomial interpolation is applied to obtain a suitable candidate optimal control sequence. Model predictive control is used to implement the optimal control in predefined control windows sequentially to achieve three-axis stability for a rest-to-rest maneuver within 0.3 orbit.
Deterministic Drift Counteraction Optimal Control for Attitude Control of Spacecraft with Time-Varying Mass
