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. Note to Practitioners-Due to the fact that many mechanical systems work in stochastic environments, disturbances cannot be avoided. It is of practical significance to investigate random MASs with mismatched disturbances. In practical application, convergence rate is an essential indicator to gauge the performance of the system. Finite-time stability (FTS) is frequently mandated to be achieved for faster convergence, higher accuracy, and better anti-disturbance. Therefore, the definition and theorem of NSPFTS are given, which simplifies the process of controller design and stability analysis. Subsequently, a novel control strategy for random MASs with mismatched disturbances is put forth, drawing upon the proposed finite-time Lyapunov theorem. By integrating the state observer and the dynamic surface control method into the backstepping control design, the proposed controller avoids the differential explosion problem that often occurs in the backstepping method, which reduces the computational burden. All followers can track the leader within a finite time. The explicit establishment of the expectation of settling time allows for the estimation of an upper bound for convergence time in practical applications. This control strategy offers a practical and viable solution for implementation in various manufacturing environments.