机器人末端臂轨迹跟踪自适应控制设计

本文提出了新颖的机器人末端臂轨迹跟踪自适应控制方法。该方法与已有的神经网络模型不同之处在于数据首先利用运动学反解求出机器人各关节旋转的角度,然后应用径向基函数自组织进行神经网络学习生成模糊规则,利用监督学习算法(SLA)、最小二乘法(LMS)、反向传播算法(BP)和聚类分析的方法在线优化控制规则以及隶属函数的参数。仿真结果表明,该方法不但规则生成的时间少,有效的防止了规则数爆炸,而且在机器人轨迹跟踪控制的应用中效果好。     

机械臂的自适应径向基函数神经网络双二次泛函最优控制

针对非线性机械臂系统中难以权衡控制能量与控制误差比重的最优控制问题,本文提出一种基于自适应径向基函数(RBF)神经网络二阶段叠加优化的双二次泛函最优求解模型,实现在非线性机械臂控制系统中用不大的控制能量来保持较小的控制误差的综合最优控制.在本文所提模型中,首先设计一种线性误差函数,作用于非线性控制方程,并采用自适应RBF网络逼近非线性控制方程中存在的不确定项,构成闭环反馈系统,实现对非线性系统的最优控制;其次,将待求参数复合成双二次泛函的解域,并设计一种新型的类递归神经网络求解该带约束条件的双二次型模型,实现模型求解的快速收敛并得其解.通过理论分析及数值仿真实例验证了所提模型能有效提高非线性系统的控制精度、稳定性、鲁棒性及自适应性,从而实现非线性系统的综合最优控制.     

A priori error estimates of a meshless method for optimal control problems of stochastic elliptic PDEs

In this paper, we study the optimal control problems of stochastic elliptic equations with random field in its coefficients. The main contributions of this work are two aspects. Firstly, a meshless method coupled with the stochastic Galerkin method is investigated to approximate the control problems, which is competitive for high-dimensional random inputs. Secondly, a priori error estimates are derived for the solutions to the control problems. Some numerical tests are carried out to confirm the theoretical results and to demonstrate the efficiency of the proposed method.     

基于径向基点插值的Chan-Vese模型图像分割算法

基于水平集方法的Chan-Vese模型是一种典型的几何活动轮廓模型,已成功应用于众多领域中的图像分割问题。为了提高该模型的演化速度和分割效果,提出了一种基于径向基点插值求解Chan-Vese模型的高效数值算法。通过用径向基点插值法逼近水平集函数,Chan-Vese模型被离散为常微分方程组初值问题并可用向前Euler法求解。该算法不需要网格单元,对水平集初始轮廓不敏感,不涉及复杂费时的重新初始化过程,并且有明确的演化终止条件,无需事先设置演化次数。实验表明该算法在没有初始轮廓时也能正确分割图像,具有很快的演化速度。     

CONORBIT: constrained optimization by radial basis function interpolation in trust regions†

This paper presents CONORBIT (CONstrained Optimization by Radial Basis function Interpolation in Trust regions), a derivative-free algorithm for constrained black-box optimization where the objective and constraint functions are computationally expensive. CONORBIT employs a trust-region framework that uses interpolating radial basis function (RBF) models for the objective and constraint functions, and is an extension of the ORBIT algorithm [S.M. Wild, R.G. Regis and C.A. Shoemaker, ORBIT: optimization by radial basis function interpolation in trust-regions, SIAM J. Sci. Comput. 30 (2008), pp. 3197–3219]. It uses a small margin for the RBF constraint models to facilitate the generation of feasible iterates, and extensive numerical tests confirm that such a margin is helpful in improving performance. CONORBIT is compared with other algorithms on 27 test problems, a chemical process optimization problem, and an automotive application. Numerical results show that CONORBIT performs better than COBYLA (Powell 1994), a sequential penalty derivative-free method, an augmented Lagrangian method, a direct search method, and another RBF-based algorithm on the test problems and on the automotive application.     

基于轨迹控制的改进的直接函数法圆弧插补算法

基于直接函数法的圆弧插补算法能够有效提高插补精度,但是在终点判别时需要对两个轴向的步数进行计算,时间较长.在对长轴终点判别方法进行研究的基础上,提出了一种改进的直接函数法的圆弧插补算法.以每步插补的连续前进轴为长轴,并以在长轴上的插补步数为判断基准,对插补点是否到达终点作出判断.该方法要求不同卦限圆弧对应不同长轴.该算...     

Frequency Optimized Computation Methods

In this paper we develop an alternative method to derive finite difference approximations of derivatives on arbitrary distrubutions of data points. The purpose is to find schemes which work for a broader range of frequencies than the usual approximations based on polynomial fitting to the expense of less accuracy for low frequencies. The numerical schemes are obtained as solutions to constrained optimizations problems in a weighted L ²-norm in the frequency domain. We examine the accuracy of these schemes and compare them with the standard approximations. To test the accuracy of the different schemes, we study dispersion errors for a simple wave equation in one space dimension. We examine the number of points per wave length which is needed in order for the relative error in the phase velocity to be below a certain bound. We also apply the technique to solve a simple two-dimensional hyperbolic equation.     

基于RBF神经网络的空间插值法在空气质量监测中的应用

针对我国现有大气监测站点数量有限且离散,采集的数据不能代表整个区域的空气质量等问题,提出基于RBF神经网络的空间插值法应用于空气质量的监测,以经纬度和邻近点污染物浓度为输入,建立插值点与地理坐标和邻近点之间的对应关系.实验结果表明:该方法具有较高的插值精度,为预测未知空间数据值提供了有效的处理方法,同时为大气污染治理和控制提供理论依据.     

无线传感器网络的系统化自适应建模

无线传感器网络的系统能耗制约着全网络的综合应用能力,其中节点有限的能量从根本上影响着传感器网络效能。针对无线传感器网络的全局能耗问题,提出了基于径向基函数神经网络以及状态空间表达的系统化建模方法。考虑到无线传感器网络的拓扑结构与分级关系, 采用径向基函数神经网络自适应实时规划系统。鉴于各传感器节点对数据的不同处理方式与能耗密切相关, 对全系统能耗建立系统化矩阵模型。仿真分析表明该模型可根据实际应用背景调整设置完成全局优化。     

采用免疫进化算法优化设计径向基函数模糊神经网络控制器

基于生物免疫系统的计算智能近年来正逐渐成为一个研究热点.针对模糊神经网络控制器难于设计的问题,提出了一种免疫进化算法用于径向基函数模糊神经网络控制器参数的优化设计.首先将控制器参数进行编码表示成个体,并由若干随机个体组成初始群体;然后模拟生物适应性免疫应答过程,通过扩展操作在群体中较优秀个体的小邻域内进行局部搜索,同时利用突变操作在较差个体的大邻域内搜索;最后将设计的控制器用于控制倒立摆系统,仿真结果验证了该控制器的有效性.     

Sliding-mode and proportional-derivative-type motion control with radial basis function neural network based estimators for wheeled vehicles

An obstacle avoidance problem of rear-steered wheeled vehicles in consideration of the presence of uncertainties is addressed. Modelling errors and additional uncertainties are taken into consideration. Controller designs for driving and steering motors are designed. A proportional-derivative-type driving motor controller and a sliding-mode steering controller combined with radial basis function neural network (RBFNN) based estimators are proposed. The convergence properties of the RBFNN-based estimators are proven by the Stone–Weierstrass theorem. The stability of the proposed control law is proven using Lyapunov stability analysis. The obstacle avoidance strategy utilising the sliding surface adjustment to an existing navigation method is presented. It is concluded that the driving velocity and steering-angle performances of the proposed control system are satisfactory.     

Reconfiguration of face expressions based on the discrete capture data of radial basis function interpolation

Compactly supported radial basis function can enable the coefficient matrix of solving weigh linear system to have a sparse banded structure,thereby reducing the complexity of the algorithm.Firstly,based on the compactly supported radial basis function,the paper makes the complex quadratic function(Multiquadric,MQ for short) to be transformed and proposes a class of compactly supported MQ function.Secondly,the paper describes a method that interpolates discrete motion capture data to solve the motion vectors of the interpolation points and they are used in facial expression reconstruction.Finally,according to this characteristic of the uneven distribution of the face markers,the markers are numbered and grouped in accordance with the density level,and then be interpolated in line with each group.The approach not only ensures the accuracy of the deformation of face local area and smoothness,but also reduces the time complexity of computing.     

基于投影寻踪的非线性鲁棒偏最小二乘法及应用

来自工业现场的数据往往具有非线性特性且包含离群点, 利用非线性偏最小二乘(partial least squares, PLS)建模易受离群点的影响. 针对这一问题, 结合径向基函数(radial basis function, RBF)网络, 本文提出了一种基于投影寻踪的非线性鲁棒PLS方法. 该方法首先利用RBF变换将自变量与因变间的非线性关系转化为线性关系; 然后利用投影寻踪算法提取变换后自变量的鲁棒偏最小二乘法成分; 最后建立鲁棒PLS成分与因变量之间的鲁棒线性回归模型. 将该方法应用于湿法冶金萃余液pH值软测量建模问题, 结果验证了其有效性.     

基于径向基函数的残缺点云数据修复

提出一种具有较强鲁棒性的残缺点云数据修复算法,借助kD tree寻找点云的缺陷边界,确定点云的缺陷区域;然后利用二次曲面的特性参数化边界点列;最后,通过径向基函数表示的插值曲面计算位于残缺区域内部的数据点,实现残缺点云数据的修复．     

真实感3D人脸快速建模研究*

现有的三维人脸建模方法存在三点不足：建模条件苛刻、建模精度不高和建模时间长。针对以上不足,提出明暗恢复形状（SFS）和局部形变模型融合的3D人脸建模方法。该方法利用SFS快速恢复3D人脸粗糙数据,得到3D轮廓脸;然后分别对人脸不同局部应用形变模型恢复其局部3D精确数据,并使用其对轮廓脸进行内插平滑处理重建出高精度3D人脸模型。实验结果表明：该方法能够获得较好的建模精度,在短时间内可以通过单幅真实图像重建出个性化的三维人脸模型。     

基于径向基函数网络的非线性离散时间系统的自适应控制

对于一类离散时间的非线性系统x(k+1)=f(x(k))+u(k)+d(k),当系统中的非线性函数f(x(k))满足线性增长条件时,首先证明了{x(k)}落入一紧集中,然后根据高斯径向基函数网络的逼近性质,给出了自适应控制器的设计方法.利用李亚普诺夫稳定性理论,证明了控制算法是全局稳定的,跟踪误差收敛于零的某一领域中.