Distributed Formation Control of Nonlinear State Delay Multi-Agent Systems with Unknown Control Direction and Communication Ranges

The paper studies the design problem of adaptive distributed formation control for nonlinear state delay multi-agent systems (MASs) with unknown control direction. The unknown nonlinear functions are approximated by radial basis function neural networks (RBFNNs), then Lyapunov-Krasovskii functional and Nussbaum-type function are introduced to solve the state time-delay and unknown control direction problems, respectively. Combining adaptive backstepping control and dynamic surface control (DSC) technique, a nonlinear formation error transformation method is used to achieve connectivity maintenance. On the basis of the Lyapunov stability theory, it is proven that all signals of the closed-loop system are semi-globally uniformly ultimately bounded (SGUBB), and tracking error converges to a small neighborhood of origin.