Distributed adaptive containment control for a class of discrete-time nonlinear multi-agent systems with uncertainties

A distributed adaptive containment control scheme is developed for a class of discrete-time multi-agent systems (MASs) under directed graphs. Each agent's model is described by nonlinear dynamics with unknown parameters that are nonlinearly coupled with the states. To deal with the uncertainties, a criterion function with weighted factor is adopted. By minimising the criterion function, a projection algorithm for each agent is designed to estimate the unknown parameters. Using the estimated parameters, an adaptive controller with only local information is designed for each agent to achieve containment control of MASs. Under the proposed distributed adaptive containment control scheme, it is guaranteed that all the leaders can finally track their reference signals and all the states of followers asymptotically converge to the convex hull formed by leaders (i.e. the convex hull formed by the reference signals). Finally, two simulation examples are given to illustrate the effectiveness of the proposed scheme.