Distributed containment control for uncertain nonlinear multi-agent systems in non-affine pure-feedback form under switching topologies

This paper considers the containment control problem of uncertain nonlinear multi-agent systems with multiple dynamic leaders under switching directed topologies. The followers are governed by a class of non-affine pure-feedback systems with arbitrary uncertainty. Implicit function and mean value theorems are employed to overcome the difficulty in controlling the non-affine pure-feedback systems and fuzzy logic systems are utilized to approximate the unknown nonlinear functions. Distributed adaptive containment controllers are proposed to guarantee that the outputs of all followers converge to the convex hull spanned by the multiple dynamic leaders. In addition, by incorporating the distributed dynamic surface control (DSC) technique, the developed containment controllers are able to eliminate the problem of “explosion of complexity” inherent in backstepping design. Based on Lyapunov stability theory, it is proved that all signals in the closed-loop systems are cooperatively semiglobally uniformly ultimately bounded (CSUUB), and the containment errors converge to a small neighborhood of the origin. An example is provided to show the effectiveness of the control approach.