Neural network-based adaptive consensus of second-order multi-agent systems with nonlinear uncertainties and unknown time delay

This paper studies the leader-following adaptive optimal neural network consensus (AONNC) of second-order multi-agent systems (SOMASs) with nonlinear uncertainties and unknown time delay. An objective function involving the squared distance error and control effort is introduced which will be minimized by the AONNC method. The controller consists of two main parts. The first linear part is based on state feedback control idea and it is designed in such a way that the linear part of each agent dynamics is stable and the objective function is minimum. The nonlinear part which is designed based on the neural network (NN) will compensate for the nonlinear uncertainties and the external disturbances. By defining the distance error between each follower and the leader and taking time derivative of it, the error dynamics of each agent is obtained. To estimate the NN gains, appropriate adaptive rules are presented. The Lyapunov stability criterion is employed to prove the asymptotic stability of SOMAS. It is proved that the time derivative of the Lyapunov function for the aforementioned AONNC method and the adaptation laws is negative and therefore, the consensus of SOMAS is achieved. To verify the AONNC protocol, a SOMAS consisting of five agents (one leader and four followers) is considered and the obtained results are discussed.