Distributed Containment Control for Multi-agent Systems in Pure-feedback Form under Switching Topologies

The distributed containment control problem is investigated for nonlinear multi-agent systems in pure-feedback form subjected to switching directed communication topologies. Based on command filtered back-stepping technology and singular-perturbation theorem, a containment controller is addressed to guarantee that the followers' outputs can converge to the convex hull spanned by multi-dynamic leaders, and the containment tracking errors between leaders and followers is semi-global practical exponential stable in the closed-loop system. A nonlinear anti-tangent filter is adopted to estimate the virtual control, avoiding the analytical deduction inherent in traditional back-stepping method and overcoming the ?circular construction problem? in non-affine pure-feedback systems. Differing from the existing back-stepping method, the proposed control scheme only requires leaders' output signals and their first derivative signals, does not need the prior knowledge of their nth order derivative signals. The stability analysis is completed via the singular perturbation theory, revealing some novel features of the underlying back-stepping method. Finally, two simulation examples are provided to illustrate the effectiveness of the control scheme.