Finite-Time Output Tracking Control for Random Multi-Agent Systems With Mismatched Disturbances

The problem of noise-to-state practically finite-time output tracking control for random multi-agent systems (MASs) subjected to mismatched disturbances is considered in this paper. Firstly, the definition of noise-to-state practically finite-time stability (NSPFTS) and its criterion are proposed for a single system described by a random differential equation (RDE). Furthermore, the NSPFTS is extended to random MASs for the first time. By integrating dynamic surface control into the backstepping approach, a new control strategy based on the distributed finite-time observer is developed for random MASs with mismatched disturbances. The differential explosion problem typically encountered in the traditional backstepping method is overcome. By using the noise-to-state practically finite-time Lyapunov theorem proposed, tracking errors of followers can be adjusted arbitrarily small within a finite time. Additionally, the upper boundness of settling time is given explicitly in probability. Finally, two examples confirm the effectiveness of the proposed control approach.