Weighted containment control for Lagrangian systems with heterogeneous interactions of cooperation and competition
Liyun Zhao, Jinchen Ji · International Journal of Control · 2020
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.