Containment control for multiple euler-lagrange systems with parametric uncertainties in directed networks
Jie Mei, Wei Ren, Guangfu Ma · 2011
In this paper, we study the distributed containment control problem for networked Lagrangian systems with multiple stationary or dynamic leaders in the presence of parametric uncertainties under a directed graph that characterizes the interaction among the leaders and the followers. When the leaders are stationary, a distributed adaptive control algorithm is proposed. We present a necessary and sufficient condition on the directed graph such that all followers converge to the stationary convex hull spanned by the stationary leaders asymptotically. As a byproduct, we show a necessary and sufficient condition on leaderless consensus for networked Lagrangian systems under a directed graph. When the leaders are dynamic, two cases are considered: i) The leaders have constant vectors of generalized coordinate derivatives; ii) The leaders have varying vectors of generalized coordinate derivatives. In the first case, we propose a distributed continuous estimator and a distributed adaptive control algorithm. In the second case, we propose a distributed adaptive control algorithm combined with distributed sliding-mode estimators. In both cases, a necessary and sufficient condition on the directed graph is presented such that all followers converge to the dynamic convex hull spanned by the dynamic leaders asymptotically.