The Radial Basis Functions Neural Network （RBFNN） is used to establish the model of a response system through the input and output data of the system. The synchronization between a drive system and the response syst...The Radial Basis Functions Neural Network （RBFNN） is used to establish the model of a response system through the input and output data of the system. The synchronization between a drive system and the response system can be implemented by employing the RBFNN model and state feedback control. In this case, the exact mathematical model, which is the precondition for the conventional method, is unnecessary for implementing synchronization. The effect of the model error is investigated and a corresponding theorem is developed. The effect of the parameter perturbations and the measurement noise is investigated through simulations. The simulation results under different conditions show the effectiveness of the method.展开更多
An adaptive integral dynamic surface control approach based on fully tuned radial basis function neural network （FTRBFNN） is presented for a general class of strict-feedback nonlinear systems,which may possess a wid...An adaptive integral dynamic surface control approach based on fully tuned radial basis function neural network （FTRBFNN） is presented for a general class of strict-feedback nonlinear systems,which may possess a wide class of uncertainties that are not linearly parameterized and do not have any prior knowledge of the bounding functions.FTRBFNN is employed to approximate the uncertainty online,and a systematic framework for adaptive controller design is given by dynamic surface control. The control algorithm has two outstanding features,namely,the neural network regulates the weights,width and center of Gaussian function simultaneously,which ensures the control system has perfect ability of restraining different unknown uncertainties and the integral term of tracking error introduced in the control law can eliminate the static error of the closed loop system effectively. As a result,high control precision can be achieved.All signals in the closed loop system can be guaranteed bounded by Lyapunov approach.Finally,simulation results demonstrate the validity of the control approach.展开更多
The method of determining the structures and parameters of radial basis function neural networks(RBFNNs) using improved genetic algorithms is proposed. Akaike′s information criterion (AIC) with generalization error t...The method of determining the structures and parameters of radial basis function neural networks(RBFNNs) using improved genetic algorithms is proposed. Akaike′s information criterion (AIC) with generalization error term is used as the best criterion of optimizing the structures and parameters of networks. It is shown from the simulation results that the method not only improves the approximation and generalization capability of RBFNNs ,but also obtain the optimal or suboptimal structures of networks.展开更多
The machining precision not only depends on accurate mechanical structure but also depends on motion compensation method. If manufacturing precision of mechanical structure cannot be improved, the motion compensation ...The machining precision not only depends on accurate mechanical structure but also depends on motion compensation method. If manufacturing precision of mechanical structure cannot be improved, the motion compensation is a reasonable way to improve motion precision. A motion compensation method based on neural network of radial basis function(RBF) was presented in this paper. It utilized the infinite approximation advantage of RBF neural network to fit the motion error curve. The best hidden neural quantity was optimized by training the motion error data and calculating the total sum of squares. The best curve coefficient matrix was got and used to calculate motion compensation values. The experiments showed that the motion errors could be reduced obviously by utilizing the method in this paper.展开更多
构造一种适用于反向传播(backpropagation,BP)神经网络的新型激活函数Lfun(logarithmic series function),并使用基于该函数的BP神经网络进行机床能耗状态的预测。首先,分析Sigmoid系列和ReLU系列激活函数的特点和缺陷,结合对数函数,构...构造一种适用于反向传播(backpropagation,BP)神经网络的新型激活函数Lfun(logarithmic series function),并使用基于该函数的BP神经网络进行机床能耗状态的预测。首先,分析Sigmoid系列和ReLU系列激活函数的特点和缺陷,结合对数函数,构造了一种非线性分段含参数激活函数。该函数可导且光滑、导数形式简单、单调递增、输出均值为零,且通过可变参数使函数形式更灵活;其次,通过数值仿真实验在公共数据集上将Lfun函数与Sigmoid、ReLU、tanh、Leaky_ReLU和ELU函数的性能进行对比;最后,使用基于Lfun函数的BP神经网络进行机床能耗状态的预测。实验结果表明,使用Lfun函数的BP神经网络相较于使用其他几种常用激活函数的网络具有更好的性能。展开更多
基金This project was supported in part by the Science Foundation of Shanxi Province (2003F028)China Postdoctoral Science Foundation (20060390318).
文摘The Radial Basis Functions Neural Network （RBFNN） is used to establish the model of a response system through the input and output data of the system. The synchronization between a drive system and the response system can be implemented by employing the RBFNN model and state feedback control. In this case, the exact mathematical model, which is the precondition for the conventional method, is unnecessary for implementing synchronization. The effect of the model error is investigated and a corresponding theorem is developed. The effect of the parameter perturbations and the measurement noise is investigated through simulations. The simulation results under different conditions show the effectiveness of the method.
基金supported by the China Postdoctoral Science Foundation (200904501035 201003548)+3 种基金the National Natural Science Foundation of China (60835001907160289101600460804017)
文摘An adaptive integral dynamic surface control approach based on fully tuned radial basis function neural network （FTRBFNN） is presented for a general class of strict-feedback nonlinear systems,which may possess a wide class of uncertainties that are not linearly parameterized and do not have any prior knowledge of the bounding functions.FTRBFNN is employed to approximate the uncertainty online,and a systematic framework for adaptive controller design is given by dynamic surface control. The control algorithm has two outstanding features,namely,the neural network regulates the weights,width and center of Gaussian function simultaneously,which ensures the control system has perfect ability of restraining different unknown uncertainties and the integral term of tracking error introduced in the control law can eliminate the static error of the closed loop system effectively. As a result,high control precision can be achieved.All signals in the closed loop system can be guaranteed bounded by Lyapunov approach.Finally,simulation results demonstrate the validity of the control approach.
文摘The method of determining the structures and parameters of radial basis function neural networks(RBFNNs) using improved genetic algorithms is proposed. Akaike′s information criterion (AIC) with generalization error term is used as the best criterion of optimizing the structures and parameters of networks. It is shown from the simulation results that the method not only improves the approximation and generalization capability of RBFNNs ,but also obtain the optimal or suboptimal structures of networks.
基金supported by the Project of National Natural Science Foundation of China(51275052)the Project of Science and Technique Development Plan of Beijing Municipal Commission of Education(KM201311232022)
文摘The machining precision not only depends on accurate mechanical structure but also depends on motion compensation method. If manufacturing precision of mechanical structure cannot be improved, the motion compensation is a reasonable way to improve motion precision. A motion compensation method based on neural network of radial basis function(RBF) was presented in this paper. It utilized the infinite approximation advantage of RBF neural network to fit the motion error curve. The best hidden neural quantity was optimized by training the motion error data and calculating the total sum of squares. The best curve coefficient matrix was got and used to calculate motion compensation values. The experiments showed that the motion errors could be reduced obviously by utilizing the method in this paper.
文摘构造一种适用于反向传播(backpropagation,BP)神经网络的新型激活函数Lfun(logarithmic series function),并使用基于该函数的BP神经网络进行机床能耗状态的预测。首先,分析Sigmoid系列和ReLU系列激活函数的特点和缺陷,结合对数函数,构造了一种非线性分段含参数激活函数。该函数可导且光滑、导数形式简单、单调递增、输出均值为零,且通过可变参数使函数形式更灵活;其次,通过数值仿真实验在公共数据集上将Lfun函数与Sigmoid、ReLU、tanh、Leaky_ReLU和ELU函数的性能进行对比;最后,使用基于Lfun函数的BP神经网络进行机床能耗状态的预测。实验结果表明,使用Lfun函数的BP神经网络相较于使用其他几种常用激活函数的网络具有更好的性能。
