Coordination motion of Lagrangian systems with multiple oscillatory leaders under diverse interaction topologies

ABSTRACT

This paper investigates coordination behaviour of Lagrangian systems with multiple dynamic leaders. Firstly, under the directed networked topology, a containment control protocol is presented, in which the communication is physically measurable. The result shows that all followers can converge to the convex hull spanned by the oscillatory leaders, if there exists at least one oscillatory leader that has a directed path to each follower. Subsequently, cluster synchronisation problem is discussed by using integral action under two kinds of network structures. One is that all of couplings among followers are positive, and the other is the existence of both positive and negative couplings in different clusters. One big superiority for introduction of integral control is that generalised velocities converge to some oscillatory orbits. Finally, numerical simulations are presented to demonstrate the effectiveness of the theoretical results.

KEYWORDS:

• Lagrangian systems
• interaction topology
• containment control
• cluster synchronisation

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

This work is supported by the National Science Foundation of China [grant number 61663035], the Baotou Science and Technology project [grant number 2017S2003-3-8].