Robust containment control of heterogeneous non-linear multi-agent systems via power series approach

In this study, the robust containment control problem of general non-linear multi-agent systems (MASs) subject to structural uncertainties is studied. The leaders are also described by general non-linear dynamics satisfying a locally quasi-Lipschitz condition and a distributed non-linear observer is designed to estimate the leaders' states for the followers. The solvability of the regulator equations associated with the non-linear dynamics of agents is normally essential for solving the containment control problem of heterogeneous MASs, but the closed-form solution of many non-linear regulator equations may not be obtained. Towards this end, the power series approach is adopted to decompose the regulator equations into a series of solvable linear equations. Based on the solution of the linear equations as the feedforward information, the distributed robust containment control scheme based on state feedback and output feedback control is proposed. The p-copy internal model is employed to compensate the parameter uncertainties of the follower agents. A numerical example is studied to demonstrate the effectiveness and efficiency of the proposed control law.