Leader-Follower Formation of Second-Order Nonlinear Multi-Agent Systems by Adaptive Neural Networks with Novel Kernel

Abstract

In this research work, a novel kernel is conceptualized with the cosine of the distances for radial basis function neural networks (RBFNNs’) for leader-follower formation control problem of second-order nonlinear systems. The adaptive RBFNNs’ acts as a function approximator and also generates the control signal. A weight tuning rule gives the estimated weights. The desired formation for a nonlinear second-order system is achieved. Switching topology is applied between the leader and followers. The results are compared with a purely Gaussian kernel based on Euclidean distances and a mixture of cosine and Gaussian kernels. The overall stability of the system is proved by the Lyapunov function. Numerical simulations show the superior performance of the novel cosine kernel.