Finite-time and Fixed-time Time-varying Formation Tracking for Multiple Euler-Lagrange Systems With Disturbances

Abstract

This article mainly tackles the finite-time time-varying formation tracking (Fin-TVFT) problem and fixed-time time-varying formation tracking (Fix-TVFT) problem of multiple Euler-Lagrange systems (MELSs) subject to the external disturbances under the directed interaction topology. The distributed estimator-based hierarchical control (EBHC) algorithms are respectively formulated to achieve the foregoing problems. Note that the settling time of Fin-TVFT depends on the initial values, but the convergence time of Fix-TVFT is independent of the initial conditions. According to the Lyapunov stability analysis, several sufficient conditions for accomplishing the Fin-TVFT and Fix-TVFT are derived. Eventually, the simulation results are exhibited in order to illustrate the feasibility of the designed algorithms.