Singularity-Free Low-Complexity Fault-Tolerant Prescribed Performance Control for Spacecraft Attitude Stabilization

This paper is concerned with the problem of fault-tolerant prescribed performance attitude stabilization for space-craft under model uncertainties and actuator failures. In most of the existing control designs for spacecraft described by the unit quaternion, the possible singularity issue of the virtual control coefficient matrix is neglected such that the controllability of the attitude subsystem cannot be warranted throughout. On the other hand, the related works depend on complex algorithms of approximation, estimation or diagnosis to deal with unknown system dynamics. In this paper, a singularity-free low-complexity fault-tolerant prescribed performance control (PPC) strategy is put forward. To exclude the singularity issue, an initialization principle of the performance envelop is devised. On this basis, a static PPC law is developed, without parameter identification, function approximation, disturbance estimation, failure detection, failure isolation, failure estimation. In place of the classical Lyapunov stability theory, a unified performance analysis framework based on proof by contradiction and the barrier Lyapunov function is constructed. It not only turns out attitude stabilization with the preassigned settling time and accuracy whenever the actuator failures happen, but also discloses the intrinsic robustness of the control system versus actuator failures and model uncertainties. A comparative study on a rigid spacecraft is performed to demonstrate the validity and advantage of our approach.