Prescribed-time adaptive bipartite time-varying formation tracking for multiple Lagrangian systems with arbitrary disturbance

This article focuses on the problem of bipartite time-varying formation tracking for multiple Lagrangian systems with prescribed-time adaptive sliding mode under the signed digraph. First, for each Lagrangian system, the local prescribed-time disturbance estimator is proposed to estimate arbitrary disturbances in the prescribed time with the condition of bounded disturbances. Then the distributed prescribed-time observers are designed to observe the position and velocity of the leader, and the consensus problem is transformed into bipartite formation tracking via introducing above observers. Based on designing two types of observers and disturbance estimators, a new prescribed-time adaptive sliding mode controller is designed to ensure the tracking errors of the sliding mode surface converge to origin in a prescribed time. Ultimately, the feasibility of the provided results is further demonstrated through numerical simulation.