## 1 Introduction  
As the research hotspot in the field of spaceflight technology, which has been intensively studied in the past decade, spacecraft formation flying has been a key technology for lots of space missions, such as distributed aperture radar, earth monitoring, and deep space observation [1, 2]. Compared with a large and complex spacecraft, a spacecraft formation flying system provides a multitude of benefits in space missions, including higher reconfiguration performance, higher reliability and redundancy, and low dependence on ground stations. Spacecraft formation control is regarded as the core technology for spacecraft formation flying with the diversification of space missions [3]. Therefore, spacecraft formation control techniques have been increasingly attracting the attention of scholars during the past two decades; many research results have been developed in the literature [4, 5]. In on-orbit spacecraft formation flying systems, various perturbations, including solar radiation pressure, atmospheric drag, and the earth's oblateness from the space environment, will result in drifts in both the formation configuration and the formation center. On the other hand, a spacecraft formation control system unavoidably manifests various types of unexpected anomalies and faults during on-orbit mission operations [6, 7]. Faults may dramatically degrade the control performance properties to the point that formation configurations may be unsatisfactory for space missions, and could even result in the loss of control of an entire spacecraft formation control system. To guarantee the high control performance, reliability, and safety of spacecraft formation flying systems, fault diagnosis and fault-tolerant control (FTC) are challenging problems that need to be handled urgently for spacecraft formation flying systems in practice. In view of these, fault diagnosis and FTC for spacecraft formation control systems have attracted considerable attention in both research and practical applications during the past decade, and great progress has been achieved in recently published work in the literature [8; 9; 10; 11; 12; 13; 14; 15; 16]. In [8], fuzzy rule-based fault diagnosis approaches were proposed for the leader-follower spacecraft formation architecture. In [9], a fault detection and diagnosis approach, based on the Lur'e differential inclusion theory and fuzzy wavelet neural network, was proposed for the propulsion subsystem of spacecraft formation. In [10], based on the linear parameter varying technique, nonlinear observers were respectively explored to detect, isolate, and estimate actuator faults in a multi-satellite formation system, and less conservative linear matrix inequality (LMI) conditions were provided for observer design. In [11], a new sub-observers-based distributed cooperative state and fault estimation framework was proposed for a formation flight of satellites with unreliable relative state determination information resulting from external disturbances and actuator faults. In this framework, a series of sub-observers were selected and configured by a decision-making supervisor that cooperatively estimated the relative states and actuator faults. In [12], considering model uncertainties, time-varying disturbances and faults in spacecraft sensors and thrusters, a traditional sliding mode control algorithm, and a non-singular terminal sliding mode control algorithm were proposed for accurate formation configuration maintenance based on variable-structure control theory. To solve the fault-tolerant precise control problem of a satellite formation flying system with various uncertainties and external disturbances, the minimum sliding mode error feedback control approach was proposed based on the concept of equivalent control error to offset the J2 perturbation and smooth out the effect of the nonlinear switching control in [13].