Abstract
A time-varying feedback control law based on backstepping is proposed for the prescribed arbitrary time stabilization and tracking for a chain of integrators. Prescribed arbitrary time control permits the convergence time to be chosen regardless of the initial conditions or system parameters. The sufficient condition is used to demonstrate Lyapunov stability for the system. Analytical results and explanations are provided for the influence of convergence time on the maximum needed control torque. Sliding mode control is paired with the time-varying feedback approach to make the control law robust to reject the bounded disturbance. The control law is then applied to a spacecraft's attitude motion that is susceptible to the bounded disturbance. A quaternion-based attitude representation is utilized to avoid mathematical singularity. The control law is written using a full quaternion with four components instead of only three in the vector part. Finally, promising numerical simulation results are presented.
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