Fully distributed containment of a class of disturbed nonlinear multi-agent systems

In this paper, the fully distributed containment problem is investigated for a class of second-order nonlinear multi-agent systems (MASs) with disturbance and uncertain control coefficient. In the dynamics of the multi-agent systems, the nonlinear term of the multi-agent systems is Lipshitz, the leaders are subject to bounded inputs, and the disturbances are also bounded. But, the Lipshitz constant, the upper bounds of the disturbances and the leaders' control inputs are unknown; thus, they cannot be used for the design of feedback control. To overcome the difficulty from such unknown bounds and uncertain coefficient, a new fully distributed adaptive protocol is proposed by combining the Lyapunov analysis and adaptive control technique, which based only on relative states of neighboring agents without using any global information, such that the states of the followers converge to the convex hull formed by the states of the leaders. Compared with the existing works, one main contribution is that only one adaptive gain is adopted in the fully distributed adaptive protocol to deal with containment problem of second-order nonlinear MASs, where four unknown parameters are involved. Two simulation examples are given to show the performance of the proposed protocol.