Neuro-Adaptive Formation Control of Nonlinear Multi-Agent Systems With Communication Delays

The paper focuses on formation control with constant communication delays for second-order, uncertain, nonlinear multi-agents with a nonsymmetric control gain matrix and an unknown control direction. The multi-agent system is modeled using an undirected graph. A three-layer neural network (NN) is employed to approximate an unknown nonlinearity. Unlike a conventional one- or two-layer NN, the three-layer NN allows the user to apriori determine the number of neurons in each layer. In this case, only the weight norms of the two consecutive outer layers are tunable, which alleviates computational complexity. The tuning law is derived using Lyapunov stability theory. The leader-following formation control problem with communication delays is addressed through a delayed integral of error variables, an NN-based control, and a robustifying term. The semi-globally uniformly ultimately bounded (SGUUB) solution of the closed-loop system is rigorously proven using a barrier Lyapunov function. To evaluate the efficiency and performance of the proposed method, simulation results are provided.