Distributed containment control for nonlinear multiagent systems in pure-feedback form

In this paper, the problem of distributed containment control for pure-feedback nonlinear multiagent systems under a directed graph topology is investigated. The dynamics of each agent are molded by high-order nonaffine pure-feedback form. Neural networks are employed to identify unknown nonlinear functions, and dynamic surface control technique is used to avoid the problem of explosion of complexity inherent in backstepping design procedure. The Frobenius norm of the ideal neural network weighting matrices is estimated, which is helpful to reduce the number of the adaptive tuning law and alleviate the networked communication burden. The proposed distributed containment controllers guarantee that all signals in the closed-loop systems are cooperatively semiglobally uniformly ultimately bounded, and the outputs of followers are driven into a convex hull spanned by the multiple dynamic leaders. Finally, the effectiveness of the developed method is demonstrated by simulation examples.