Relationship between Levels of Persistent Excitation,Architectures of Neural Networks and Deterministic Learning Performance

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• 英文论文题名：Relationship between Levels of Persistent Excitation,Architectures of Neural Networks and Deterministic Learning Performance
• 论文作者：Tongjia Zheng ; Cong Wang
• 英文论文作者：Tongjia Zheng ; Cong Wang ; School of Automation Science and Technology ; South China University of Technology ; Guangdong Key Laboratory of Biomedical Engineering ; South China University of Technology
• 年：2017
• 作者机构：School of Automation Science and Technology,South China University of Technology;Guangdong Key Laboratory of Biomedical Engineering,South China University of Technology;
• 英文论文关键词：PE condition ; level of excitation ; architecture of neural networks ; neural network identification ; deterministic learning
• 会议召开时间：2017-07-26
• 会议录名称：第36届中国控制会议论文集（B）
• 英文会议录名称：Proceedings of the 36th Chinese Control Conference（B）
• 语种：英文
• 分类号：TP183
• 学会代码：KZLL
• 会议名称：第36届中国控制会议
• 会议地点：中国辽宁大连
• 主办单位：中国自动化学会控制理论专业委员会
• 学会名称：中国自动化学会控制理论专业委员会
• 页数：6
• 文件大小：269k
• 原文格式：D
• 会议级别：全国

摘要

Based on the concept of persistent excitation(PE), a deterministic learning algorithm is proposed for neural network(NN)-based identification of nonlinear systems recently. This paper investigates the quantitative relationship between the PE levels(including the level of excitation), the architectures of NNs and the convergence properties of deterministic learning,which is motivated by a practical problem of how to construct the NNs in order to guarantee sufficient level of excitation and identification accuracy for specific system trajectories. The results on PE levels are utilized to analyze the deterministic learning performance. It is proven that by increasing the density of NN centers, the approximation capabilities of NNs increase but the level of excitation decreases, which means that a trade-off exists in the convergence accuracy when adjusting NN architectures.
Based on the concept of persistent excitation(PE), a deterministic learning algorithm is proposed for neural network(NN)-based identification of nonlinear systems recently. This paper investigates the quantitative relationship between the PE levels(including the level of excitation), the architectures of NNs and the convergence properties of deterministic learning,which is motivated by a practical problem of how to construct the NNs in order to guarantee sufficient level of excitation and identification accuracy for specific system trajectories. The results on PE levels are utilized to analyze the deterministic learning performance. It is proven that by increasing the density of NN centers, the approximation capabilities of NNs increase but the level of excitation decreases, which means that a trade-off exists in the convergence accuracy when adjusting NN architectures.

引文

[1]R.M.Sanner and J.J.E.Slotine.Gaussian networks for direct adaptive control.IEEE Transactions on Neural Networks,3(6):837–863,1992.
    [2]M.Wang,X.Liu,and P.Shi.Adaptive neural control of purefeedback nonlinear time-delay systems via dynamic surface technique.IEEE Transactions on Systems,Man,and Cybernetics,Part B(Cybernetics),41(6):1681–1692,Dec 2011.
    [3]H.Wang,K.Liu,X.Liu,B.Chen,and C.Lin.Neural-based adaptive output-feedback control for a class of nonstrictfeedback stochastic nonlinear systems.IEEE Transactions on Cybernetics,45(9):1977–1987,Sept 2015.
    [4]S.Lu and T.Basar.Robust nonlinear system identification using neural-network models.IEEE Transactions on Neural Networks,9(3):407–429,1998.
    [5]P.A.Ioannou and J.Sun.Robust adaptive control.Courier Corporation,2012.
    [6]Robert M Sanner and Jean-Jacques E Slotine.Stable recursive identification using radial basis function networks.In American Control Conference,1992,pages 1829–1833.IEEE,1992.
    [7]D.Gorinevsky.On the persistency of excitation in radial basis function network identification of nonlinear systems.IEEE Transactions on Neural Networks,6(5):1237–1244,1995.
    [8]A J Kurdila,Francis J Narcowich,and Joseph D Ward.Persistency of excitation in identification using radial basis function approximants.SIAM journal on control and optimization,33(2):625–642,1995.
    [9]C.Wang and D.J.Hill.Learning from neural control.IEEE Transactions on Neural Networks,17(1):130–146,2006.
    [10]C.Wang and D.J.Hill.Deterministic learning and rapid dynamical pattern recognition.IEEE Transactions on Neural Networks,18(3):617–630,2007.
    [11]C.Wang and T.Chen.Rapid detection of small oscillation faults via deterministic learning.IEEE Transactions on Neural Networks,22(8):1284–1296,2011.
    [12]Chengzhi Yuan and Cong Wang.Persistency of excitation and performance of deterministic learning.Systems&Control Letters,60(12):952–959,2011.
    [13]A.Loria and E.Panteley.Uniform exponential stability of linear time-varying systems:revisited.Systems&Control Letters,47(1):13–24,2002.
    [14]L.Ljung.System identification:Theory for the user,ptr prentice hall information and system sciences series,1999.
    [15]P.Saratchandran G.Huang and N.Sundararajan.An efficient sequential learning algorithm for growing and pruning rbf(gap-rbf)networks.IEEE Transactions on Systems,Man,and Cybernetics,Part B:Cybernetics,34(6):2284–2292,2004.
    [16]H.Yu,P.D.Reiner,T.Xie,T.Bartczak,and B.M.Wilamowski.An incremental design of radial basis function networks.IEEE Transactions on Neural Networks and Learning Systems,25(10):1793–1803,2014.
    [17]H.Han,Q.Chen,and J.Qiao.An efficient self-organizing{RBF}neural network for water quality prediction.Neural Networks,24(7):717–725,2011.
    [18]H.Chen,Y.Gong,and X.Hong.Online modeling with tunable rbf network.IEEE Transactions on Cybernetics,43(3):935–947,June 2013.
    [19]J.Lian,J.Hu,and S.H.Zak.Variable neural adaptive robust control:A switched system approach.IEEE Transactions on Neural Networks and Learning Systems,26(5):903–915,May2015.
    [20]J.Park and I.W.Sandberg.Universal approximation using radial-basis-function networks.Neural computation,3(2):246–257,1991.
    [21]M.D.Buhmann.Radial basis functions.Acta Numerica 2000,9:1–38,2000.
    [22]J.D.Ward F.J.Narcowich and H.Wendland.Sobolev bounds on functions with scattered zeros,with applications to radial basis function surface fitting.Mathematics of Computation,74(250):743–764,2005.
    [23]C.Wang and D.J.Hill.Deterministic learning theory for identification,recognition,and control,volume 32.CRC Press,2009.
    [24]O.E.Rossler.An equation for continuous chaos.Physics Letters A,57(5):397–398,1976.