Conventional RBF neuron network is usually based on Gaussian activation function with single width for each activation function.This feature restricts neuron performance for modeling the complex nonlinear problems.To accommodate limitation of a single scale

this paper applies neural network with similar but yet different activation functionHBF(Hyper Basis Function).The state for nonlinear systems is estimated by using HBF neural networks.Combined with RBF (Radial Basis Function) networks

the structure of networks

the form of its basis functions and its influence on HBF(Hyper Basis Function) are analyzed.Decision tree algorithm is used to determine the network center.Then a design method of adaptive observer based on HBF neural networks is proposed.The Lyapunov function is introduced to prove the stability and the conditions of the bounded error of the observer.And this HBF neural network is turned out to observe system state very well by simulation.