Formation Control of Nonlinear Multi-Agent Systems Using Three-Layer Neural Networks

This paper considers a leader-following formation control problem for heterogeneous, second-order, uncertain, input-affine, nonlinear multi-agent systems modeled by a directed graph. A tunable, three-layer neural network (NN) is proposed with an input layer, two hidden layers, and an output layer to approximate an unknown nonlinearity. Unlike commonly used trial and error efforts to select the number of neurons in a conventional NN, in this case an \textit{a priori} knowledge allows one to set up the number of neurons in each layer. The NN weights tuning laws are derived using the Lyapunov theory. The leader-following and formation control problems are addressed by a robust integral of the sign of the error (RISE) feedback and a NN-based control. The RISE feedback term compensates for unknown leader dynamics and the unknown, bounded disturbance in the agent error dynamics. The NN-based term compensates for the unknown nonlinearity in the dynamics of multi-agent systems, and semi-global asymptotic tracking results are rigorously proven using the Lyapunov stability theory. The results of the paper are compared with two previous results to evaluate the efficiency and performance of the proposed method.