Cooperative adaptive fault‐tolerant tracking control for a class of multi‐agent systems with actuator failures and mismatched parameter uncertainties

Abstract

This study addresses the cooperative fault-tolerant tracking control problem for a class of multi-agent systems subject to mismatched parameter uncertainties, external disturbances and actuator faults including loss of effectiveness, outage and stuck. The communication network is undirected connected graph with a fixed topology. It is assumed that the actuator efficiency factors, the upper bounds of the unparametrisable time-varying stuck faults and disturbance, are unknown. Different from the traditional centralised fault-tolerant tracking control problem, only part of the follower nodes can obtain the information of leader directly. On the basis of the local state information of neighbouring agents, a novel cooperative fault-tolerant tracking control scheme by using adaptive mechanism is proposed. By introducing the estimates of controller parameters driven by neighbourhood tracking errors, it is shown that not only the actuator faults in the follower nodes can be compensated, but also the global tracking objective can be achieved. Furthermore, it is proved that all closedloop signals are bounded and all follower nodes asymptotically tracking to the leader can be achieved in the presence of actuator faults, external disturbances and mismatched parameter uncertainties. Finally, a numerical example is given to show the effectiveness of the proposed control scheme. IntroductionRecently, research on cooperative control of multi-agent systems (MAS) has received considerable attention from various scientific fields. It has potential applications in broad areas including the formation of flight of satellites, sensor networks, mobile robots, and so forth [1]. A number of effective approaches have been made to study the emergence of cooperative control of MAS, with many profound results established [2-4]. According to whether the desired consensus values are determined by exogenous inputs, the cooperative control of MAS are often classified as cooperative regulator problem, called consensus, and the cooperative tracking problem, known as synchronisation [5]. In literature, a series of papers addressed the cooperative tracking of general linear MAS, which referred as consensus tracking with switching topologies [6, 7], adaptive coupling strategy [8], consensus for discrete-time MAS [9], optimal control method [10] and so on. As well known, in practical applications, many MAS to be controlled have both uncertainties and external disturbances. Distributed consensus tracking problems are investigated in [11,12] for higher-order Lipschitz-type node dynamics networks under fixed undirected topology and switching directed topologies, respectively. In [13], distributed robust control problem for MAS with parameter uncertainties and external disturbances is investigated, a sufficient condition in terms of LMIs can ensure closed-loop networks is quadratically stable. On the basis of neuroadaptive method, a model reference cooperative tracking controller using state information of neighbours is designed for uncertain dynamical sys...

Distributed adaptive fault‐tolerant consensus tracking of multi‐agent systems against time‐varying actuator faults

“…On the other hand from Fig. 7, it can be seen that the tracking errors using the method in [32] also cannot asymptotically converge to zero since both multiple delayed state perturbations and time-varying fault efficiency factors cannot be dealt with in that paper. These figures illustrates that the distributed adaptive faultytolerant consensus tracking controller in this paper is effective even if time-varying actuator fault, mismatched uncertainty, multiple delayed state perturbations and disturbances exist simultaneously.…”

“…time-varying bias fault, respectively. Recently in [32], a new consensus protocol has been proposed for linear multi-agent system for time-varying stuck fault, but the considered multiplicative fault factor is constant. In this paper, the more general time-varying fault model (5) is given, which includes both time-varying additive fault and time-varying multiplicative fault.…”

“…Remark 3: Assumptions 1 and 2 are necessary in the robust fault-tolerant control literature to completely compensating the stuck-actuator faults and disturbances, which has been studied in [24][25][26]32]. Assumption 3 is a basic assumption to ensure the controllability of the plant and the existence of a nominal solution for the actuator failure compensation problem [22][23][24][25][26].…”

“…Remark 4: Unlike [32], the coupling consensus protocol gain c, which is dependent on all the eigenvalues of Laplacian matrix of the communication graph, should be used to design fault-tolerant control for constant fault. While for time-varying fault, motivated by Li et al [16], in this paper the coupling gaind i (t) is updated online by (14).…”

“…time-invariant loss of effectiveness fault), Zuo et al [30] and Chen et al [31] have studied the adaptive fault-tolerant consensus tracking problem of MASs using different methods. For more general fault model including both addictive fault and multiplicative fault, the adaptive fault-tolerant consensus tracking problem of linear multi-agent systems has been discussed in [32], where the multiplicative factor of fault is assumed to be time invariant.…”