This paper mainly focuses on the fixed-time consensus (FXC) control problem for nonlinear multi-agent systems (MASs). For the cases of leader-following and leaderless, two adaptive discontinuous protocols are designed, respectively, to realize our control goals. Common adaptive control protocols always significantly increase the dimension of the considered system model, while the protocols presented here only require two adaptive update laws and are therefore simpler to apply in the engineering control. Moreover, no additional conditions are required to ensure that the system can achieve FXC successfully, except for some necessary assumptions. Simulation examples also illustrate that these two protocols are effective.

The multi-agent-based supply chain network is a dynamic system consisting of multiple subchains connected by information flows, material flows and capital flow, etc. The consensus of multi-agent systems is often applied to the cooperation between subchains and inventory management in supply chain networks. Considering the ubiquitous external disturbances, this paper mainly considers the fixed-time consensus of a stochastic three-echelon multi-agent-based supply chain system. A nonlinear feedback fixed-time control protocol is constructed for ensuring the consensus of the considered supply chain network. Using the stability theory of stochastic differential equations, sufficient conditions for the fixed-time consensus and the upper bound estimation of the settling time are obtained. Finally, the validity of the control protocol and the correctness of the theoretical analysis are revealed by numerical simulation.