Predefined-time backstepping attitude tracking control of a spacecraft under inertia-matrix uncertainty and external disturbances

The attitude tracking problem for a rigid spacecraft is considered in the presence of inertia-matrix uncertainty and bounded external disturbances. The rotational motion is described by modified Rodrigues parameters. Parametric uncertainty and external actions are combined into a lumped disturbance, which is estimated by a nonlinear extended state observer whose estimation error converges in finite time. A predefined-time tracking law is then synthesized by the backstepping method. Its parameterization allows the required upper bound of the transient duration to be assigned directly and independently of the initial conditions. Sufficient conditions for practical predefined-time stability of the closed-loop system are established using the direct Lyapunov method. Numerical simulations are performed for three-axis spacecraft motion with periodic disturbances and a time-varying inertia matrix. Comparison with a fixed-time controller demonstrates that the proposed approach provides an adjustable transient duration, small attitude-tracking errors, and bounded control torques. Simulations with several values of the predefined-time parameter additionally confirm that the settling-time bound can be selected through one design parameter. The obtained results indicate that the developed control law is suitable for high-accuracy spacecraft attitude maneuvers under model uncertainty and external perturbations.

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