Improved Finite-Time Sliding Mode Control for Multi-Agent Systems Under Fuzzy Topologies

In this paper, a novel sliding mode control (SMC) method is designed to investigate the finite-time consensus tracking (FTCT) problem of the second-order leader-following multi-agent systems (MASs) with imprecise communication topology of each agent. First, a T-S fuzzy model is introduced to characterize the inexact communication topology of the leader-following MASs. Moreover, a fuzzy SMC law is designed to ensure the reachability of the constructed sliding mode surface (SMS). Meanwhile, in light of the partitioning strategy, sufficient conditions for FTCT of the leader-following MASs are established. It is worth mentioning that the distributed SMC method proposed in this paper is based on the unknown sliding gain, which can greatly reduce the conservatism. Finally, the simulation study on a group of single-link robots and a numerical simulation demonstrate the feasibility of proposed control method. Note to Practitioners—This paper aims to ensure the transient performance and good robustness of second-order multi-agent systems. Generally, the classic nonlinear control method, sliding mode control (SMC), is accompanied by a certain level of conservativeness due to its fixed sliding gain matrix. Moreover, excessive conservatism may prevent the proposed control strategy from being implemented in practical engineering. To address this issue, we formulate an improved finite-time SMC framework to reduce the conservatiness. We also designed an improved algorithm based on genetic algorithm (GA) and linear matrix inequalities (LMIs) to solve the difficulties brought by the new control algorithm, thereby facilitating its practical implementation and enhancing the overall performance of the second-order multi-agent systems.