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Fuzzy smooth support vector machine with different smooth functions 认领 引用 被引量：5
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作者 Chuandong Qin Sanyang Liu 《Journal of Systems Engineering and Electronics》 SCIE EI CSCD 2012年第3期460-466,共7页
Smooth support vector machine （SSVM） changs the normal support vector machine （SVM） into the unconstrained op- timization by using the smooth sigmoid function. The method can be solved under the Broyden-Fletcher-G... Smooth support vector machine （SSVM） changs the normal support vector machine （SVM） into the unconstrained op- timization by using the smooth sigmoid function. The method can be solved under the Broyden-Fletcher-Goldfarb-Shanno （BFGS） algorithm and the Newdon-Armijio （NA） algorithm easily, however the accuracy of sigmoid function is not as good as that of polyno- mial smooth function. Furthermore, the method cannot reduce the influence of outliers or noise in dataset. A fuzzy smooth support vector machine （FSSVM） with fuzzy membership and polynomial smooth functions is introduced into the SVM. The fuzzy member- ship considers the contribution rate of each sample to the optimal separating hyperplane and makes the optimization problem more accurate at the inflection point. Those changes play a positive role on trials. The results of the experiments show that those FSSVMs can obtain a better accuracy and consume the shorter time than SSVM and lagrange support vector machine （LSVM）. 展开更多
关键词 smooth support vector machine （SSVM） fuzzy sig- moid function polynomial smooth function fuzzy membership Broyden-Fletcher-Gddfarb-Shanno （BFGS）.
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OPTIMAL ERROR BOUNDS FOR THE CUBIC SPLINE INTERPOLATION OF LOWER SMOOTH FUNCTIONS(1) 认领 引用
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作者 Ye Maodong Zhejiang University,China 《Analysis in Theory and Applications》 1993年第4期46-54,共9页
In this paper,the kernel of the cubic spline interpolation is given.An optimal error bound for the cu- bic spline interpolation of lower smooth functions is obtained.
关键词 As OPTIMAL ERROR BOUNDS FOR THE CUBIC SPLINE INTERPOLATION OF LOWER SMOOTH FUNCTIONS 十义 义人
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Smoothing Approximations for Some Piecewise Smooth Functions 认领 引用 被引量：4
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作者 Hao Wu Peng Zhang Gui-Hua Lin 《Journal of the Operations Research Society of China》 EI CSCD 2015年第3期317-329,共13页
In this paper,we study smoothing approximations for some piecewise smooth functions.We first present two approaches for one-dimensional case:a global approach is to construct smoothing approximations over the whole do... In this paper,we study smoothing approximations for some piecewise smooth functions.We first present two approaches for one-dimensional case:a global approach is to construct smoothing approximations over the whole domain and a local approach is to construct smoothing approximations within appropriate neighborhoods of the nonsmooth points.We obtain some error estimate results for both approaches and discuss whether the smoothing approximations can inherit the convexity of the original functions.Furthermore,we extend the global approach to some multiple dimensional cases. 展开更多
关键词 Piecewise smooth function Smoothing approximation Error estimate
EXTENSION OF SMOOTHING FUNCTIONS TO SYMMETRIC CONE COMPLEMENTARITY PROBLEMS 认领 引用 被引量：2
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作者 Liu Yongjin Zhang Liwei Liu Meijiao 《Applied Mathematics(A Journal of Chinese Universities)》 2007年第2期245-252,共8页
The paper uses Euclidean Jordan algebras as a basic tool to extend smoothing functions, which include the Chen-Mangasarian class and the Fischer-Burmeister smoothing functions, to symmetric cone complementarity proble... The paper uses Euclidean Jordan algebras as a basic tool to extend smoothing functions, which include the Chen-Mangasarian class and the Fischer-Burmeister smoothing functions, to symmetric cone complementarity problems. Computable formulas for these functions and their Jacobians are derived. In addition, it is shown that these functions are Lipschitz continuous with respect to parameter # and continuously differentiable on J × J for any μ 〉 0. 展开更多
关键词 symmetric cone complementarity problem smoothing function Euclidean Jordan algebra non-interior continuation method
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New smooth gap function for box constrained variational inequalities 认领 引用
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作者 张丽丽 李兴斯 《Applied Mathematics and Mechanics(English Edition)》 SCIE EI 2013年第1期15-26,共12页
A new smooth gap function for the box constrained variational inequality problem （VIP） is proposed based on an integral global optimality condition. The smooth gap function is simple and has some good differentiable... A new smooth gap function for the box constrained variational inequality problem （VIP） is proposed based on an integral global optimality condition. The smooth gap function is simple and has some good differentiable properties. The box constrained VIP can be reformulated as a differentiable optimization problem by the proposed smooth gap function. The conditions, under which any stationary point of the optimization problem is the solution to the box constrained VIP, are discussed. A simple frictional contact problem is analyzed to show the applications of the smooth gap function. Finally, the numerical experiments confirm the good theoretical properties of the method. 展开更多
关键词 box constrained variational inequality problem （VIP） smooth gap function,integral global optimality condition
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Template-based smoothing functions for data smoothing in Geodesy 认领 引用 被引量：1
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作者 M.Kiani 《Geodesy and Geodynamics》 2020年第4期300-306,共7页
This paper is aimed at the derivation of a discrete data smoothing function for the discrete Dirichlet condition in a regular grid on the surface of a spheroid.The method employed here is the local L^2-seminorm minimi... This paper is aimed at the derivation of a discrete data smoothing function for the discrete Dirichlet condition in a regular grid on the surface of a spheroid.The method employed here is the local L^2-seminorm minimization,through Euler-Lagrange method,for the Beltrami operator.The method results in a weighted average of the surrounding points in a te mplate based on the first order Taylor expansion of the unknown function under consideration.The coefficients of the weighted average are calculated and used to smooth the Geoid height data in Iran,derived from the EGM2008 geopotential model. 展开更多
关键词 Minimization problem Regular grid Linear composition Beltrami operator Smoothing function
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Effect of Chaihu Shugan decoction on gastric smooth muscle cell apoptosis in rats with functional dyspepsia 认领 引用 被引量：3
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作者 Xinchao Shangguan Jianghong Ling +4 位作者 Jing Deng Lijun Zeng Yuqin Zhang Tianyi Xie Yujiao Wang 《广西医科大学学报》 CAS 2017年第4期481-485,共5页
Objective:To investigate the effect of Chaihu Shugan decoction(CSD)on gastric smooth muscle cells(GSMCs)apoptosis in rats with functional dyspepsia(FD).Methods:48Sprague-Dawley(SD)rats were randomly assigned into six ... Objective:To investigate the effect of Chaihu Shugan decoction(CSD)on gastric smooth muscle cells(GSMCs)apoptosis in rats with functional dyspepsia(FD).Methods:48Sprague-Dawley(SD)rats were randomly assigned into six groups:a normal control group,a model group,apositive control(domperidone)group and low-,middle-and high-dose CSD groups.A rat model of FD was established by constantly squeezing their tails.The rats were administered CSD(0.16g/mL,0.32g/mL,0.64g/mL)or domperidone(0.3 g/L)via intragastric gavage for four weeks.The gastric emptying rate was detected at 4 weeks post-administration.Apoptosis of GSMCs was determined by terminal deoxynucleotidyl transferase dUTP nick end labeling(TUNEL)staining and the mitochondrial morphology was observed by transmission electron microscopy.The expression of Bcl-2and Bax was measured by immunohistochemistry.Results:FD resulted in marked reduction of gastric emptying rate,severe gastric tissue damage and mitochondria injury,but were reversed by CSD treatment(P<0.05).The apoptosis-induced protein Bax was markedly down-regulated by CSD,whereas the expression of the anti-apoptotic Bcl-2 protein was notably increased(P<0.05).Furthermore,CSD could protect the FD rats against GSMCs apoptosis manifested by a decreased in TUNEL-positive cells(P<0.05).Conclusion:CSD could alleviate GSMCs apoptosis in FD rats,possibly by the modulation of Bcl-2 and Bax expression,and the suppression of mitochondria injury. 展开更多
关键词 胃平滑肌细胞 治疗方法 胃组织 重度损伤
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A NEW FORMULATION OF BERNSTEIN-BEZIER BASED SMOOTHNESS CONDITIONS FOR pp FUNCTIONS 认领 引用
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作者 Hong, Dong 《Analysis in Theory and Applications》 1995年第2期67-75,共9页
In this note, we establish a new formulation of smoothness conditions for piecewise polynomial (: =pp) functions in terms of the B-net representation in the general n-dimensional setting. It plays an important role fo... In this note, we establish a new formulation of smoothness conditions for piecewise polynomial (: =pp) functions in terms of the B-net representation in the general n-dimensional setting. It plays an important role for 2-dimensional setting in the constructive proof of the fact that the spaces of polynomial splines with smoothness rand total degree k≥3r+2 over arbitrary triangulations achieve the optimal approximation order with the approximation constant depending only on k and the smallest angle of the partition in [5]. 展开更多
关键词 A NEW FORMULATION OF BERNSTEIN-BEZIER BASED SMOOTHNESS CONDITIONS FOR pp FUNCTIONS
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Approximation of Multivariate Functions with a Certain Mixed Smoothness by Entire Functions 认领 引用
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作者 Wang Heping Sun Yongsheng 《Northeastern Mathematical Journal》 1995年第4期454-466,共13页
In this paper.we consider the approximation in the Lq(■)metric for some function classes with a certain mixed smoothness defined on■by the subspaces of Lq(■)which consist of entire functions whose spectrals l... In this paper.we consider the approximation in the Lq(■)metric for some function classes with a certain mixed smoothness defined on■by the subspaces of Lq(■)which consist of entire functions whose spectrals lie in some step hyperbolic crosses,and obtain some asymptotic estimates for the best approximation quantities. 展开更多
关键词 Approximation Function with Mixed Smoothness Entire Function
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A New Unified Path to Smoothing Nonsmooth Exact Penalty Function for the Constrained Optimization 认领 引用
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作者 Bingzhuang Liu 《Open Journal of Optimization》 2021年第3期61-70,共10页
We propose a new unified path to approximately smoothing the nonsmooth exact penalty function in this paper. Based on the new smooth penalty function, we give a penalty algorithm to solve the constrained optimization ... We propose a new unified path to approximately smoothing the nonsmooth exact penalty function in this paper. Based on the new smooth penalty function, we give a penalty algorithm to solve the constrained optimization problem, and discuss the convergence of the algorithm under mild conditions. 展开更多
关键词 Penalty Function Constrained Optimization Smoothing Method Optimal Solution
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Simulation of Oil-Water Flow in Shale Oil Reservoirs Based on Smooth Particle Hydrodynamics 认领 引用 被引量：1
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作者 Qin Qian Mingjing Lu +2 位作者 Feng Wang Aishan Li Liaoyuan Zhang 《Fluid Dynamics & Materials Processing》 EI 2022年第4期1089-1097,共9页
A Smooth Particle Hydrodynamics(SPH)method is employed to simulate the two-phase flow of oil and water in a reservoir.It is shown that,in comparison to the classical finite difference approach,this method is more stab... A Smooth Particle Hydrodynamics(SPH)method is employed to simulate the two-phase flow of oil and water in a reservoir.It is shown that,in comparison to the classical finite difference approach,this method is more stable and effective at capturing the complex evolution of this category of two-phase flows.The influence of several smooth functions is explored and it is concluded that the Gaussian function is the best one.After 200 days,the block water cutoff for the Gaussian function is 0.3,whereas the other functions have a block water cutoff of 0.8.The effect of various injection ratios on real reservoir production is explored.When 14 and 8 m3/day is employed,the water breakthrough time is 130 and 170 days,respectively,and the block produces 9246 m3 and 6338 m3 of oil cumulatively over 400 days. 展开更多
关键词 SPH oil-water two-phase flow smooth function flow simulation
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基于分数阶累积量的加权双曲复合函数平滑l0范数DOA估计方法 认领 引用
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作者 刘小松 陈玥琦 +3 位作者 单泽彪 王安妮 于艳鑫 苏成志 《电子测量与仪器学报》 EI CSCD 北大核心 2026年第5期78-86,共9页
针对现有波达方向(direction of arrival,DOA)估计算法无法同时抑制α稳定分布噪声和高斯色噪声问题,提出了一种基于分数阶累积量和加权双曲复合函数的平滑l0范数的DOA估计算法。首先,利用分数阶累积量的半不变性以及对α稳定分布和... 针对现有波达方向(direction of arrival,DOA)估计算法无法同时抑制α稳定分布噪声和高斯色噪声问题,提出了一种基于分数阶累积量和加权双曲复合函数的平滑l0范数的DOA估计算法。首先,利用分数阶累积量的半不变性以及对α稳定分布和高斯分布不敏感的特性,抑制α稳定分布和高斯色噪声。然后,将分数阶累积量矩阵进行向量化处理,并推导出基于分数阶累积量的稀疏DOA重构模型。最后,构造双曲复合函数对l0范数进行平滑逼近,并通过调节逼近因子实现平滑性与陡峭性的自适应权衡。同时,引入加权矩阵,对真实信号源对应位置进行加权增强,其余位置权值被抑制,进一步突出稀疏解的结构特征。在此基础上,采用梯度下降与投影相结合的双层迭代策略求解加权平滑l0优化问题,从而获得目标信号的DOA值。仿真实验结果表明,在α稳定分布与高斯色噪声混合且混合信噪比低至0的条件下,所提算法DOA估计的均方根误差为0.5164°,充分验证了其在复杂噪声背景下的有效性和高精度。 展开更多
关键词 波达方向估计 分数阶累积量 双曲复合函数 平滑l0范数
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基于自适应改进小波阈值限幅滤波的平抑风电波动策略 认领 引用
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作者 李培强 刘抒睿 欧阳旭 《电气工程学报》 CSCD 北大核心 2026年第2期358-370,共13页
基于风电功率的随机性与波动性对电网运行稳定性的负面影响,提出了一种加入限幅环节的改进小波阈值函数滤波,并通过改进的麻雀搜索算法对改进小波阈值函数的调节系数进行不同工业场景下的寻优,得到适应不同需求的波动平抑后并网功率曲... 基于风电功率的随机性与波动性对电网运行稳定性的负面影响,提出了一种加入限幅环节的改进小波阈值函数滤波,并通过改进的麻雀搜索算法对改进小波阈值函数的调节系数进行不同工业场景下的寻优,得到适应不同需求的波动平抑后并网功率曲线。对风电功率进行平抑后,以储能出力积累与波动平抑欧氏距离指标对不同场景下的并网功率曲线进行评估。算例研究表明,所提改进小波阈值函数限幅滤波能够很好平抑风电波动,并使并网功率限制在我国1 min、10 min尺度的MPFR限值以下,且可以适应不同工业需求调节目标函数权重值得到相应的并网功率曲线;同时验证了NTSSA算法在寻优性能上的优越性。 展开更多
关键词 风电功率 小波阈值滤波 阈值函数 波动平抑
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On n-K Width of Certain Function Classes Defined by Linear Differential Operators in L_2 Space 认领 引用
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作者 吴嘎日迪 包那 《Chinese Quarterly Journal of Mathematics》 1999年第4期27-31,共5页
Let M(u) be an N function, A=D r+∑r-1k=0a k(x)D k a linear differential operator and W M(A) the Sobolev Orlicz class defined by M(u) and A. In this paper we give the asymptotic estimates of the n K width d n(W M(... Let M(u) be an N function, A=D r+∑r-1k=0a k(x)D k a linear differential operator and W M(A) the Sobolev Orlicz class defined by M(u) and A. In this paper we give the asymptotic estimates of the n K width d n(W M(A),L 2[0,1]) . 展开更多
关键词 linear operator smooth function class width
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New family of piecewise smooth support vector machine 认领 引用 被引量：5
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作者 Qing Wu Leyou Zhang Wan Wang 《Journal of Systems Engineering and Electronics》 SCIE CSCD 2015年第3期618-625,共8页
Support vector machines （SVMs） have been extensively studied and have shown remarkable success in many applications. A new family of twice continuously differentiable piecewise smooth functions are used to smooth th... Support vector machines （SVMs） have been extensively studied and have shown remarkable success in many applications. A new family of twice continuously differentiable piecewise smooth functions are used to smooth the objective function of uncon- strained SVMs. The three-order piecewise smooth support vector machine （TPWSSVMd） is proposed. The piecewise functions can get higher and higher approximation accuracy as required with the increase of parameter d. The global convergence proof of TPWSSVMd is given with the rough set theory. TPWSSVMd can efficiently handle large scale and high dimensional problems. Nu- merical results demonstrate TPWSSVMa has better classification performance and learning efficiency than other competitive base- lines. 展开更多
关键词 support vector machine （SVM） piecewise smooth function smooth technique bound of convergence.
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基于自适应裁剪的深度学习差分隐私保护方案 认领 引用 被引量：1
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作者 程宇航 尚涛 +1 位作者 姜亚彤 杜瑞忠 《信息安全研究》 CSCD 北大核心 2026年第6期490-502,共13页
针对深度学习模型在差分隐私保护下存在效用下降以及理论隐私保护效果与实际效果偏差的问题,提出基于自适应裁剪的深度学习差分隐私保护方案.方案通过4步机制实现优化:梯度自适应裁剪自适应调整梯度裁剪阈值控制训练时梯度大小,实现对... 针对深度学习模型在差分隐私保护下存在效用下降以及理论隐私保护效果与实际效果偏差的问题,提出基于自适应裁剪的深度学习差分隐私保护方案.方案通过4步机制实现优化:梯度自适应裁剪自适应调整梯度裁剪阈值控制训练时梯度大小,实现对后续添加噪声大小的控制;分组标签选择,通过选取梯度最小的组作为隐私保护对象,训练该分组能够得到更准确的隐私损失;优化的隐私损失计算通过结合基于子采样的高斯机制,减小模型隐私损失计算的开销;优化的梯度自适应下降,通过调整条件平滑参数实现梯度的自适应下降,提升模型的可用性.在VGG(visual geometry group)架构下训练MNIST,CIFAR-10,Medical-MNIST数据集,结果表明采用该方案训练后模型准确率分别为81.08%,72.30%,67.91%,相比传统的差分隐私随机梯度下降(differential privacy stochastic gradient descent,DPSGD)方法分别提升15.60%,10.60%,9.71%,相比近年常用的Nadam算法分别提升0.63%,2.50%,4.40%,模型训练效率分别提升35.5%,39.4%. 展开更多
关键词 深度学习 差分隐私 梯度自适应裁剪 标签选择 平滑损失函数
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On n-K Width of Certain Function Classes Defined by Linear Differential Operators in L2 Space 认领 引用 被引量：2
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作者 吴嘎日迪 包那 《Chinese Quarterly Journal of Mathematics》 1999年第4期27-31,共5页
Let M(u) be an N function, A=D r+∑r-1k=0a k(x)D k a linear differential operator and W M(A) the Sobolev Orlicz class defined by M(u) and A. In this paper we give the asymptotic estimates of the n K width d n(W M(... Let M(u) be an N function, A=D r+∑r-1k=0a k(x)D k a linear differential operator and W M(A) the Sobolev Orlicz class defined by M(u) and A. In this paper we give the asymptotic estimates of the n K width d n(W M(A),L 2[0,1]) . 展开更多
关键词 linear operator smooth function class width
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基于改进D* Lite与APF算法的机器人动态路径规划 认领 引用
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作者 赵卫东 倪永顺 陈昊然 《安徽工业大学学报（自然科学版）》 CAS 2026年第2期181-190,共10页
针对动态环境下机器人路径规划存在的搜索时间长、路径不平滑及避障性能不足等问题,提出一种融合D* Lite算法与人工势场法(artificial potential field,APF)的路径平滑优化算法。首先,通过优化D* Lite算法的启发函数和键值算子提... 针对动态环境下机器人路径规划存在的搜索时间长、路径不平滑及避障性能不足等问题,提出一种融合D* Lite算法与人工势场法(artificial potential field,APF)的路径平滑优化算法。首先,通过优化D* Lite算法的启发函数和键值算子提升搜索效率;进而改进APF斥力函数并引入随机虚拟障碍物,以解决机器人易陷入局部最优的问题,并通过引力-斥力协同机制实现目标趋近于动态避障。算法融合实现了动态环境下路径的快速搜索与高效避障,为进一步提升路径规划的实用性与运动流畅性,采用剪枝策略去除冗余节点以降低运算复杂度,并减少不必要转向以降低路径曲折度;在此基础上引入三次B样条曲线对路径进行平滑处理,消除尖锐拐点,生成符合运动学规律的平滑路径。仿真实验结果表明:相较于传统D* Lite算法,本文算法在简单、复杂和狭窄通道三类典型环境中,搜索时间分别减少13.3%,9.3%和11.5%,路径平滑度与避障能力显著提升,实现了高效全局规划和局部动态避障的有效结合,显著缩短了路径搜索时间,验证了算法的优越性与实用性,为动态环境下机器人高效、平滑与鲁棒的路径规划提供了有效解决方案。 展开更多
关键词 D*Lite算法 APF算法 路径规划 动态避障 启发函数 路径平滑 实时规划 智能机器人
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分段复合幂次趋近律的滑模控制 认领 引用
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作者 刘旭 智亚丽 +2 位作者 张燕 孙先涛 陈文杰 《控制理论与应用》 EI CAS CSCD 北大核心 2026年第3期671-676,共6页
针对传统幂次趋近律作用下的滑模控制中存在的收敛速度缓慢和抖振现象,本文在自适应趋近律和幂次趋近律的基础上,选择分段函数的形式,提出一种分段复合幂次趋近律.通过引入随系统状态变化的平滑函数以及对传统幂次趋近律的改进,保证系... 针对传统幂次趋近律作用下的滑模控制中存在的收敛速度缓慢和抖振现象,本文在自适应趋近律和幂次趋近律的基础上,选择分段函数的形式,提出一种分段复合幂次趋近律.通过引入随系统状态变化的平滑函数以及对传统幂次趋近律的改进,保证系统在各个阶段都具有较快的趋近速率;同时,本文证明所提出的分段复合幂次趋近律能够快速收敛且到达滑模面时无抖振现象,并在系统存在外界干扰时能够收敛于稳态误差界;最后,通过对比仿真证明所提趋近律的有效性和优越性. 展开更多
关键词 滑模控制 平滑函数 分段复合幂次趋近律 稳态误差界
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基于改进REA*算法的机器人自适应路径规划 认领 引用 被引量：1
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作者 朱玲 李靖 张朝辉 《系统仿真学报》 EI CAS CSCD 北大核心 2026年第2期332-345,共14页
为提高机器人全局路径规划的计算效率及路径平滑度,提出了一种基于改进单边矩形扩展(rectangle expansion A*,REA*)算法的机器人自适应路径规划策略。在障碍物周围设置缓冲区保障机器人运行的安全性;以矩形单边扩展形成的通行区间作为... 为提高机器人全局路径规划的计算效率及路径平滑度,提出了一种基于改进单边矩形扩展(rectangle expansion A*,REA*)算法的机器人自适应路径规划策略。在障碍物周围设置缓冲区保障机器人运行的安全性;以矩形单边扩展形成的通行区间作为运算单位,结合双向交替搜索策略加速路径规划的效率;基于势场理论,引入向量形式优化评价函数自适应快速避障;提出一种新的路径规划策略以优化路径平滑度。仿真结果表明:与经典的A*算法及REA*算法等相比,该算法能够在更短时间内找到较短且平滑的路径。 展开更多
关键词 路径规划 REA*算法 双向交替搜索 自适应评价函数 路径平滑度
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