Finite-Time $\mathcal{L}_{2}$ Leader–Follower Consensus of Networked Euler–Lagrange Systems With External Disturbances

This paper is concerned with finite-time L <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> leader-follower consensus of networked Euler-Lagrange systems in the presence of external disturbances. A distributed finite-time L <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> control protocol is proposed by using backstepping design such that a group of follower agents modeled by Euler-Lagrange systems can follow a desired leader agent and achieve leader-follower consensus in finite time. Moreover, the finite-time L <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> gain is less than or equal to a prescribed value. A simulation example of a network composed of seven two-link manipulators is given to show the effectiveness of the theoretical results.