Distributed adaptive containment control for a class of discrete-time nonlinear multi-agent systems with unknown parameters and control gains

This paper considers the containment control problem for the discrete-time nonlinear multi-agent systems with unknown parameters and completely unknown control gains. In this paper, the dynamics of each agent are nonlinearly coupled with the neighbors’ states. To deal with the unknown parameters and control gains, a projection-type estimation algorithm is designed with the singular value avoided in the estimated control gains. The bounded estimation errors of parameters and control gains are guaranteed by the convergence analysis based on the Lyapunov approach. Then, using the estimated parameters and control gains, a distributed adaptive control protocol with only local information is designed for multi-agent systems. Under the proposed control protocol, the containment of multi-agent systems is guaranteed from a novel viewpoint of the absorbing Markov chain. Furthermore, simulations are carried out to illustrate the effectiveness of the proposed containment control protocol.