Distributed adaptive fixed-time consensus tracking for second-order multi-agent systems using modified terminal sliding mode

This paper investigates the fixed-time consensus tracking problems for second-order multi-agent systems with unknown external disturbances. Firstly, a fixed-time terminal sliding mode (FTTSM) is proposed, which can avoid the singularity problem. Then, two continuous distributed consensus tracking control laws with adaptive updating laws are designed respectively, in which the upper bounds of external disturbances are not required. It is proved that the two control laws can both guarantee the consensus tracking errors converge into the desired regions including the origin in fixed time. A simulation example is given to demonstrate the effectiveness of proposed methods.