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International audience; The objective of Fault-tolerant Control (FTC) is to minimize the effect of faults on systems performance (stability, trajectory tracking, etc.). However, the majority of the existing FTC methods continue to force the system to follow the pre-fault trajectories without considering the reduction in available control resources caused by actuator faults. Forcing the system to follow the same trajectories as before fault occurrence may result in actuator saturation and system's instability. Thus, pre-fault objectives should be redefined in function of the remaining resources to avoid potential saturation. The main contribution of this paper is a flatness-based trajectory planning/re-planning method that can be combined with any active FTC approach. The work considers the case of over-actuated systems where a new idea is proposed to evaluate the severity of faults occurred. In addition, the trajectory planning/re-planning approach is formulated as an optimization problem based on the analysis of attainable efforts domain in fault-free and fault cases. The proposed approach is applied to two satellite systems in \textit{rendezvous} mission

We are generating residuals for linear fault diagnosis and isolation which are 1. robust with respect to a large variety of additive disturbances, A reader who is already familiar with this algebraic setting may directly proceed to § 3. The numerous examples on various aspects of diagnosis, like the previous one, are written on the other hand in such a way that they may be understood by anyone who is not mastering those mathematical tools. We hope therefore that our results might be understood by a large community. 2. working in closed-loop, even with uncertain parameters. Several examples with their computer simulations, including a concrete case-study of a two mass system, are enlightening our viewpoint. Our methods, which are mainly of algebraic flavour (module theory, differential algebra, and operational calculus), are borrowed from recent works on control and identification.