Fault-tolerant control of jump linear systems with discrete mode observations and its application to spacecraft magnetic attitude control

This work is concerned with control of Markovian jump-linear systems, and its applications 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 which requires an exponentially growing computational burden is presented, and a suboptimal controller that only requires knowledge of the current mode measurement is proposed. The suboptimal 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 performance of the suggested control algorithm is illustrated through extensive Monte-Carlo simulations on a simple numerical example. A more realistic fault-toletant spacecraft magnetic attitude controller is developed based on the proposed approach. The attitude controller succeeds in achieving small pointing errors while mitigating the destabilizing effect of corrupted mode observations and being computationally efficient.