Design of distributed adaptive control for a class of discrete-time multi-agent systems with nonlinearity and uncertainty

In this paper, a distributed adaptive control method is considered for a class of discrete-time multi-agent systems with nonlinearity and uncertainty. Each agent is affected by its neighbors, and there is a hidden agent as the leader in multi-agent systems who knows the desired reference signal. However, other agents are aware of neither the reference signal nor the existence of the hidden leader and leadership. In order to deal with uncertainty, a criteria function for each agent, which is consist of a weighted square combination of state errors and parameter errors with time- varying weighting factor, is adopted. By minimizing the criteria function, we propose a projection algorithm for each agent to estimate unknown parameters. Furthermore, we design a distributed adaptive controller for each agent using the information of its neighbors. Under the distributed adaptive control, the rigorous mathematical proof is presented to demonstrate that all the agents ultimately track the desired reference signal. Finally, simulation results are given to illustrate the theoretical results.