Fault-tolerant spacecraft magnetic attitude control

This work is concerned with the development of a reliable fault-tolerant control algorithm. The analysis and control design approaches belong to the realm of optimal control theory for Markovian jump-linear systems. The general jump-linear optimal control problem and solution under full information is presented. Then, an extended problem is formulated where the assumption of perfect information on the mode is relaxed and replaced with the assumption of discrete mode observations. And the a priori probabilities for correct and for wrong mode detections are assumed known. An optimal solution to the extended problem is developed and a novel suboptimal controller that approximates the optimal infinite-dimensional solution using only the current mode measurement is suggested. The proposed suboptimal controller is a finite memory controller, and it possess some of the classical Linear Quadratic regulator features such as recursion, linear state feedback and state quadratic optimal cost-to-go. The performance of the suggested algorithm is illustrated through extensive Monte-Carlo simulations of a simple numeric example and of a realistic fault-tolerant spacecraft magnetic attitude control. The suggested suboptimal controller is shown to succeed in mitigating the destabilizing effect of corrupted mode observations while being computationally efficient.