Fault-Tolerant Spacecraft Magnetic Attitude Control

This work is concerned with the development of a control algorithm for Markovian jump-linear systems, and its application to fault-tolerant spacecraft magnetic attitude control. For completeness, the jump-linear quadratic optimal controller with full state and mode information is presented. Relaxing the assumption of perfect mode information, a similar optimal control problem is formulated where the mode is observed via discrete measurements. The elements of the measurement matrix, i.e. the probabilities for correct and wrong mode observations are assumed known. The optimal controller is developed, which requires an exponentially growing computational burden, and a suboptimal controller is proposed that only requires knowledge of the current mode measurement. This controller is finite memory and possess some of the classical linear quadratic regulator features such as the linear state feedback structure and a state quadratic optimal cost-to-go. The performances of the suggested algorithm are illustrated through extensive Monte-Carlo simulations on a simple numerical example. A realistic fault-tolerant spacecraft magnetic attitude controller is developed based on the proposed approach. The attitude controller succeeds in mitigating the destabilizing effect of corrupted mode observations while being computationally efficient.