Distributed adaptive three‐dimension formation control based on improved RBF neural network for non‐linear multi‐agent time‐delay systems.

Based on the improved radial basis function (RBF) neural networks, the distributed three‐dimension formation control scheme in the presence of dynamic uncertainties is studied for non‐linear multi‐agent systems with time delay. A virtual leader which tracks the desired signal is followed by all agents adaptively. Linear reduced‐order observers are designed on the basis of absolute and local state errors of each agent. The local state error and absolute state error are generated between neighbouring agents and each individual agent in formation, respectively. The time delay for each agent in the formation can be offset by designing a Lyapunov function, which can simplify the controller design. To deal with non‐linear dynamic uncertainties and unavoidable disturbance, improved RBF neural networks are employed. In comparison with traditional RBF neural networks, improved RBF neural networks can provide better convergence performance. Subsequently, the formation controller is designed and the stability of the systems is validated by using a new Lyapunov function. Numerical simulation is conducted to demonstrate the effectiveness of the proposed method for non‐linear multi‐agent time‐delay systems. [ABSTRACT FROM AUTHOR]