Finite‐time and fixed‐time tracking consensus for multi‐agent systems with disturbances via integral sliding mode control

Abstract By combining sliding mode control and adaptive control methods, distributed finite‐time and fixed‐time tracking consensus problems for multi‐agent systems with uncertain disturbances are invested, where the leader has an external bounded input unknown to all followers. First, a new integral sliding mode function that has good robustness to bounded uncertain disturbances is designed to ensure that the system can reach the sliding mode surface in a fixed time. Second, based on the fact that system can reach the sliding mode surface, a distributed static consensus control protocol is proposed, guaranteeing that each follower can keep up with a time‐varying leader with external bounded input in finite time. Third, in order to eliminate the limitation that control gains depend on certain global information, an adaptive finite‐time protocol is further designed in a thoroughly distributed fashion. It is noteworthy that the above settling time depends on the initial states and may reach infinity as the initial states grow. Fourth, fixed‐time control protocols are developed, guaranteeing that the settling time is bounded. Both static and adaptive cases are also explored. Theoretical analyses show that the proposed finite‐time and fixed‐time tracking consensus protocols are all feasible. Finally, four simulation examples are supplied to verify the effectiveness of the proposed protocols.