1. Faculty of Aerospace Engineering, Shenyang Aerospace University, Shenyang, Liaoning 110136, China;
2. College of Information Engineering, Beijing Institute of Petrochemical Technology, Beijing 102617, China
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 function—HBF(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.
[1] 高立娥,刘卫东,路尧.X字型舵水下航行器故障诊断观测器设计与仿真研究[J].弹箭与制导学报,2008,28(4):222-224. Gao Li-e,Liu Wei-dong,Lu Yao.Failure diagnose observer design and simulation for X-type rudder plane of underwater vehicle[J].Journal of Projectiles,Rockets,Missiles and Guidance,2008,28(4):222-224.(in Chinese)
[2] 宋玉琴,章卫国,刘小雄.基于RBF神经网络观测器飞控系统故障诊断[J].计算机仿真,2010,27(3):85-88. Song Yu-qin,Zhang Wei-guo,Liu Xiao-xiong.Fault diagnosis based on RBF neural network observer in flight control system[J].Computer Simulation,2010,27(3):85-88.(in Chinese)
[3] 王振华,张淼,沈毅.卫星姿态控制系统执行器故障检测与分离[J].哈尔滨工业大学学报,2013,45(2):72-76. Wang Zhen-hua,Zhang Miao,Shen Yi.Actuator fault detection and isolation for the attitude control system of satellite[J].Journal of Harbin Institute of Technology,2013,45(2):72-76.(in Chinese)
[4] 张袅娜,张德江,李兴广.基于RBF神经网络的鲁棒滑模观测器设计[J].系统工程与电子技术,2008,30(12):2455-2457. Zhang Niao-na,Zhang De-jiang,Li Xing-guang.Design of robust sliding mode observer based on RBF neural network[J].Systems Engineering and Electronics,2008,30(12):2455-2457.(in Chinese)
[5] 黄宜军,熊炎,刘宏兵.基于小波网络观测器的飞控系统故障诊断[J].弹箭与制导学报,2006,26(3):225-227. Huang Yi-jun,Xiong Yan,Liu Hong-bing.Research on fault diagnosis for flight control systems based on wavelet network observer[J].Journal of Projectiles,Rockets,Missiles and Guidance,2006,26(3):225-227.(in Chinese)
[6] Friedhelm Schwenker,Hans A.Kestler,Gu Ènther Palm.Three learning phases for radial-basis-function networks[J].Neural Networks,2001,14(4-5):439-458.
[7] CHENG Caixia,SUN Fuchun,ZHOU Xinquan.One fire detection method using neural networks[J].Tsinghua Science and Technology,2011,16(1):31-35.
[8] Dipak,M.Adhyaru.State observer design for nonlinear systems using neural network[J].Applied Soft Computing,2012,12(8):2530-2537.
[9] 武宏伟,戴琼海,王普,等.基于神经网络的非线性系统的观测器设计[J].清华大学学报(自然科学版),2000,40(3):44-47. Wu Hong-wei,Dai Qiong-hai,Wang Pu,et.al.Neural-network-based observers for nonlinear systems[J].Journal of Tsinghua University(Science and Technology),2000,40(3):44-47.(in Chinese)
[10] M Valls,R Aler,O Fernandez.Using a Mahalanobis-like distance to train radial basis neural networks[J].Computational Intelligence and Bioinspired Systems.2005,3512:257-263.
[11] Sergiy A Vorobyov,Andrzej Cichocki.Hyper radial basis function neural networks for interference cancellation with nonlinear processing of reference signal[J].Digital Signal Processing,2001,11(3):204-221.
[12] Najdan Vukovic',Zoran Miljkovic'.A growing and pruning sequential learning algorithm of hyper basisfunction neural network for function approximation[J].Neural Networks,2013,46(10):210-226.
[13] 李爱军,罗四维,黄华,等.基于决策树的神经网络[J].计算机研究与发展,2005,42(8):1312-1317. Li Ai-jun,Luo Si-wei,Huang Hua,et.al.Decision tree based neural network design[J].Journal of Computer Research and Development,2005,42(8):1312-1317.(in Chinese)
[14] 徐志超,周玉国,于凤满.基于改进神经网络的非线性系统观测器设计[J].微型机与应用,2011,30(8):76-78. Xu Zhi-chao,Zhou Yu-guo,Yu Feng-man.Design of observers for nonlinear systems based on improved neural-network[J].Microcomputer & Its Applications,2011,30(8):76-78.(in Chinese)
[15] Ferdose Ahammad Shaik,Shubhi Purwar,Bhanu Pratap.Real-time implementation of Chebyshev neural network observer for twinrotor control system[J].Expert Systems with Applications,2011,38(10):13043-13049.
2015, Vol. 43 
