Variable-Step Time-Delay Control for Proactive Aperiodic Spacecraft Attitude Control

Abstract

This paper addresses proactive aperiodic spacecraft attitude control under model uncertainty, environmental disturbances, and actuator degradation. To this end, we develop Variable step Time Delay Control (VTDC), which jointly designs robust feedback control and control-update scheduling rather than treating them as separate components. Inspired by adaptive stepsize regulation in Runge Kutta integration, VTDC structures the local control error to scale with the realized timestep. Using sliding manifold based Time Delay Control, the resulting System Time Delay Error (TDE), which reflects local model and uncertainty variations, is shown to be quadratically bounded by the control interval. This relation yields a closed form feedback law that enlarges or reduces the subsequent interval to regulate the TDE magnitude. The next update time is therefore determined algebraically without continuous trigger monitoring, future state prediction, or iterative search. The resulting variable step closed loop admits bounded timesteps and step ratios, excludes Zeno behavior, and renders the sliding variable uniformly ultimately bounded. Nonlinear spacecraft attitude control simulations demonstrate accurate tracking with low scheduling cost under representative uncertainties and disturbances.