Robust adaptive backstepping attitude and vibration control with L2-gain performance for flexible spacecraft under angular velocity constraint

This paper proposes an angular velocity bounded robust adaptive control design for attitude maneuver and vibration reduction in the presence of external disturbances and uncertainties in the inertia matrix. The control design is Lyapunov based to ensure closed-loop stability, boundedness of system states and tracking error convergence. Specifically, an adaptive controller based on backstepping technique with the assumption of bounded elastic vibrations is first designed that ensures the equilibrium points in the closed-loop system uniform ultimate bounded stability in the presence of unknown inertia matrix and bounded disturbances, incorporating constraints on individual angular velocity. The prescribed robust performance is also evaluated by L2-gain, less than any given small level, from a torque level disturbances signal to a penalty output. Then this controller is redesigned such that this assumption is released by using an elastic vibration estimator, which supplies their estimates. The external torque disturbances attenuation along with estimate errors with respect to the performance measure are also ensured in the L2-gain sense and the induced vibrations can be actively reduced as well. The novelty of our approach is in the strategy to construct such a Lyapunov function under bounded angular velocity recursively that ensures not only stability of a tracking error system but also an L2-gain constraint. Compared with the conventional methods, the proposed scheme guarantees not only the stability of the closed-loop system, but also the good performance as well as the robustness. Simulation results for the spacecraft model show that the precise attitudes control and vibration suppression are successfully achieved.