Estimator-Based Lag-Bipartite Time-Varying Formation Tracking for a Class of Euler-Lagrange Systems Using Predefined Time Control Method

This paper investigates the lag-bipartite time-varying formation tracking (LBTVFT) problem of Euler-Lagrange (EL) systems with predefined time convergence ability under directed signed digraph, in which both the parametric uncertainties and external disturbances are considered. Different from the issue of time-varying formation tracking with only cooperative interactions, this paper considers the case where coexists both the cooperative interactions and antagonistic interactions. The predefined-time hierarchical control algorithm is constructed to settle the above-mentioned problem. What's more, an estimator-based algorithm is built to guarantee that the estimated states of followers are agreement with the state of virtual leader within a preset time. Eventually, based on the assumptions that the signed digraph is structurally balance, the predefined-time LBVFT problem of EL systems is solvable via the presented hierarchical control law. Simulation examples are performed in the end to illustrate the effectiveness of theoretical results.