Finite‐time cooperative‐tracking control for networked Euler–Lagrange systems

Abstract

This study investigates the finite-time cooperative-tracking problem for a class of networked Euler-Lagrange systems with a leader-follower structure, where the leader has an active dynamics and only a subset of the followers have access to the leader system. A novel framework for the design of finite-time cooperative-tracking controller is proposed by using sliding-mode control theory and graph theory. First, a finite-time sliding-mode tracking protocol is proposed for the networked Lagrange systems in the presence of bounded model uncertainties and external disturbances. Under the condition that the bounds of the model uncertainties and external disturbances are unknown, adaptive finite-time cooperative-tracking protocol is then presented. The finite convergence time is also estimated. Finally, we analyse the tracking performance of the networked uncertain Lagrange systems under the action of a continuous control protocol, which guarantees that the tracking errors converge to an arbitrarily small bound around zero in finite time. Simulation examples are presented to show the effectiveness of the obtained theoretical results.