PDE-based prescribed performance adaptive attitude and vibration control of flexible spacecraft

Abstract

This article presents a prescribed performance adaptive control scheme for the attitude tracking and vibration reduction of flexible spacecraft modeled by partial differential equations (PDEs). First, the original constrained problem is converted to an equivalent unconstrained one by adopting a prescribed error transformation. Then, a boundary control torque law and a boundary control force law are developed to track the desired attitude and reduce the vibration, respectively. Moreover, the parametric adaptation technique is integrated with the boundary control laws to estimate the disturbances. The closed-loop system is evaluated to be asymptotically stable through the Lyapunov stability theorem and LaSalle's invariance principle. The developed controller has two distinctive features as follows. One is the controller can guarantee the attitude tracking error and tip deformation always satisfy the prescribed performance constraints. Another is the controller can acquire the strong robustness owing to the feedforward disturbance compensation. Lastly, the derived results are demonstrated by simulated studies.