# Observer-Based Distributed Fault Detection for Heterogeneous Multi-Agent Systems
## 1 Introduction  
Recently, a large amount of literature on cooperative control of multi-agent systems (MAS) has emerged, which investigate this problem from different aspects, such as event-triggered and finite-time cooperative control [1, 2]. Besides homogeneous MAS, research on heterogeneous MAS is also significant. As an effective method to realise cooperative control of heterogeneous MAS, for instance, a network of unmanned aerial vehicles (UAVs) with different dynamics, cooperative output regulation (COR) has attracted intensive research attention during the past decade [3, 4, 5, 6], which was based on output regulation theory, where the influence of mismatched disturbance generated by an exosystem could be completely rejected via converting mismatched forms into matched forms [7]. Specifically, [PERSON] and [PERSON] considered the condition that only partial information of an exosystem matrix was accessible to each agent, where a distinct estimator network was proposed to cooperatively estimate the value of the exosystem state [8]. As some agents may destroy other healthy agents due to the influence of unexpected faults, security operation of heterogeneous MAS has attracted some researchers' attention. Existing security operation schemes of heterogeneous MAS are passive, where the fault tolerant COR is ensured by the designed passive fault tolerant controllers in each agent. In [9], [PERSON] et al. designed a distributed adaptive fault tolerant control law to attenuate partial loss of actuator effectiveness faults. Furthermore, they considered the condition that actuators suffered from both partial loss of effectiveness faults and stuck faults [10, 11]. Besides designing passive fault tolerant control laws for each agent, detecting and removing faulty agents is the other effective method to ensure the security operation of MAS. Hence, some literature on FD schemes for MAS has emerged during the past decade. The basic idea is to design an additional FD algorithm for MAS, and run the FD and control algorithms simultaneously; the FD algorithm will locate and remove faulty agents intime, where the FD algorithm could be seen as a redundant algorithm to make the MAS operate well. In [12], [PERSON] et al. proposed a centralised FD scheme for a group of unmanned vehicles, a bank of observers for FD were installed in one vehicle to monitor the remaining vehicles, where the observers needed to utilise all the nodes' information. Furthermore, they considered the condition that agents suffered from external disturbances [13]. In [14], the authors proposed an FD scheme for linear MAS based on sliding mode fault estimators, where the design of fault estimators also utilised all the nodes' input information. In summary, centralised FD schemes require one agent to have ability to obtain all the nodes' information, which is contradicted with the distributed nature of MAS. Hence, researchers start considering distributed FD, where each agent just needs to have ability to obtain itself and its neighbours' measurable information. [PERSON] and [PERSON] et al. proposed a distributed FD scheme for a group of double integrators based on unknown input observer (UIO) [15; 16], where the disturbance decoupling idea was widely utilised [17; 18]. The basic idea was to adopt a distributed consensus law for each agent, and construct some FD observers for the MAS closed-loop system in one agent to judge whether a fault occurred in itself or its neighbours, then the utilisation or influence of agents' control inputs for FD results was avoided. Furthermore, the authors proposed a distributed FD scheme for second-order MAS with uncertain communication topology, where the design process of some agent's FD observers just utilised local topology information [19]. As above framework possesses distributed characteristics, some researchers have extended above framework to MAS with different kinds of agent dynamics. [PERSON] et al. designed robust FD observers for a group of discrete-time double integrators with both process and measurement noise [20].