Weighted containment control for Lagrangian systems with heterogeneous interactions of cooperation and competition

Abstract

The paper investigates the weighted containment control problem of Lagrangian systems with cooperative–competitive weighted interactions. Networked systems consist of multiple leaders and followers in different groups, and the dynamics of multiple leaders are governed by Euler–Lagrange (EL) equations. By considering the interactions of different intensity among Lagrangian agents, we propose a distributed adaptive controller with differentiators over the newly introduced cooperative–competitive weighted network. It is found that the Lagrangian followers can converge to the dynamic convex hull spanned by leaders' weighted coordinates, as long as every topology formed by the leaders' group or followers' group is interactively balanced, every follower obtains at least one leader's information and each follower is weight-product balanced. Simulation results are finally presented to validate the proposed control scheme.

Keywords:

• Lagrangian systems
• weighted containment motion
• cooperative–competitive weighted network

Acknowledgments

This work is supported by the National Science Foundation of China (Grant Nos. 62063025, 61663035), the Natural Science Foundation of Inner Mongolia Autonomous Region of China (Grant Nos. 2019MS01001, 2019MS07002, 2018MS06017), and the China Scholarship Council (Grant No. 201808155059).

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

This work is supported by the National Science Foundation of China [grant numbers 62063025, 61663035], the Natural Science Foundation of Inner Mongolia Autonomous Region of China [grant numbers 2019MS01001, 2019MS07002, 2018MS06017], and the China Scholarship Council [grant number 201808155059].