Robust adaptive formation control for nonlinear multi-agent systems with range constraints

This paper studies the adaptive distributed formation control design for pure feedback nonlinear multi-agent systems with state time-delay. Neural networks (NNs) are adopted to approximate the unknown nonlinear functions, then Lyapunov–Krasovskii functional and Nussbaum-type function are introduced to solve the state time-delay and unknown control direction problems, respectively. When considering the limitations of communication and collision, a nonlinear error transformation method is developed to achieve the collision avoidance and connectivity maintenance. Combining adaptive backstepping control and dynamic surface control technique, a robust adaptive NN predetermined time formation tracking control method is developed, which demonstrates that all signals of the closed-loop system are semi- globally uniformly ultimately bounded, and formation tracking error converges to a small neighborhood of origin. Finally, the simulation results are provided to illustrate the effectiveness and feasibility of the developed control method and theory.