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Distributed containment control for multiple-agent systems in nonlinear pure-feedback form via singular perturbation analysis

The paper considers the distributed containment control problem of nonlinear multi-agent systems in pure-feedback form under switching directed communication topologies. A singular-perturbation-based command filtered back-stepping technology is addressed to design containment controller, while overcoming the “circular construction problem” in non-affine pure-feedback systems. A anti-tangent filter is proposed to estimate the virtual control and avoid the analytical deduction inherent in traditional back-stepping method. The stability analysis is completed via the singular perturbation theory, revealing some novel features of the underlying back-stepping. The distributed containment control can guarantee followers' outputs converge to the convex hull spanned by multiple dynamic leaders, and the containment tracking errors between leaders and followers in the overall closed-loop system is semi-global practical exponential stable. Finally, a simulation example is provided to illustrate the effectiveness of the control technology.