Weighted bipartite containment motion of Lagrangian systems with impulsive cooperative–competitive interactions

Abstract

The present paper investigates weighted bipartite containment motion of networked Lagrangian systems with instantaneous cooperative–competitive interactions. A control scheme is proposed by introducing an auxiliary oscillatory system to each agent, where every Lagrangian system can obtain different levels of positive and negative information from its neighbors only at some impulsive time moments. Based on the generalized Barbalat’s lemma and Lyapunov stability theory, some conditions for the networked structure, the coupling strengthen, and the impulsive time interval are developed to guarantee that the followers can converge to the weighted intervals, which are determined by every leader’s weighted state and its symmetric weighted state. Finally, seven two-link manipulators are used to illustrate the performance of the proposed schemes.