Abstract
In this paper, the leader-following consensus problem of first-order nonlinear multi-agent systems (FONMASs) with external disturbances is studied. Firstly, a novel distributed fixed-time sliding mode manifold is designed and a new static event-triggered protocol over general directed graph is proposed which can well suppress the external disturbances and make the FONMASs achieve leader-following consensus in fixed-time. Based on fixed-time stability theory and inequality technique, the conditions to be satisfied by the control parameters are obtained and the Zeno behavior can be avoided. In addition, we improve the proposed protocol and propose a new event-triggering strategy for the FONMASs with multiple leaders. The systems can reach the sliding mode surface and achieve containment control in fixed-time if the control parameters are designed carefully. Finally, several numerical simulations are given to show the effectiveness of the proposed protocols.
Highlights
In the past several years, more and more researchers are interested in cooperative control of multi-agent systems (MASs) because of its robustness, flexible deployment and high efficiency
In the distributed consensus problem, the existing results of MASs can be roughly divided into three categories according to the number of leaders: leaderless consensus [4,5,6], leaderfollowing consensus [7,8,9] and containment control of multiple leaders [10,11]
By using integral terminal sliding mode control (SMC), the fixed-time consensus tracking issue for second-order MASs was investigated under the influence of interference signals in [33]
Summary
In the past several years, more and more researchers are interested in cooperative control of multi-agent systems (MASs) because of its robustness, flexible deployment and high efficiency. By using integral terminal SMC, the fixed-time consensus tracking issue for second-order MASs was investigated under the influence of interference signals in [33] In these works [29,30,31,32,33], all control protocols were continuously updated. SMC method combination with event-triggered control mechanism are introduced to design the distributed protocol in this paper, which can effectively suppress the disturbances and achieve consensus in fixed-time. According to the stability theory of fixed-time, we can prove that the consensus can be reached in fixed-time and the upper bound estimation of settling time is regardless of the initial conditions of MASs. The containment control for FONMASs with multiple leaders is considered, in which a generalized event-triggered integral SMC protocol is designed and the controller is updated only at some discrete instants. The symbol ⊗ denotes the Kronecker product of matrices. diag(·) represents the diagonal matrix
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