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approximation-error-ADP-based optimal tracking control for chaotic systems with convergence proof

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Chinese Physics B 2013年第9期22卷 305-311页

作者：宋睿卓肖文栋孙长银魏庆来 School of Automation and Electrical Engineering University of Science and Technology Beijing The State Key Laboratory of Management and Control for Complex Systems Institute of AutomationChinese Academy of Sciences

In this paper, an optimal tracking control scheme is proposed for a class of discrete-time chaotic systems using the approximation-error-based adaptive dynamic programming （ADP） algorithm. Via the system transformation, the optimal tracking problem is transformed into an optimal regulation problem, and then the novel optimal tracking control method is proposed. It is shown that for the iterative ADP algorithm with finite approximation error, the iterative performance index functions can converge to a finite neighborhood of the greatest lower bound of all performance index functions under some convergence conditions. Two examples are given to demonstrate the validity of the proposed optimal tracking control scheme for chaotic systems.

关键词： chaotic systems approximation error adaptive dynamic programming optimal tracking control

Carlson iterating rational approximation and performance analysis of fractional operator with arbitrary order

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Chinese Physics B 2017年第4期26卷 66-74页

作者：何秋燕余波袁晓 College of Electronics and Information Engineering Sichuan University College of Physics and Engineering Chengdu Normal University

The performance analysis of the generalized Carlson iterating process,which can realize the rational approximation of fractional operator with arbitrary order,is presented in this *** reasons why the generalized Carlson iterating function possesses more excellent properties such as self-similarity and exponential symmetry are also explained.K-index,P-index,O-index,and complexity index are introduced to contribute to performance *** nine different operational orders and choosing an appropriate rational initial impedance for a certain operational order,these rational approximation impedance functions calculated by the iterating function meet computational rationality,positive reality,and operational *** they are capable of having the operational performance of fractional operators and being physical *** approximation performance of the impedance function to the ideal fractional operator and the circuit network complexity are also exhibited.

关键词： fractional calculus fractional operator generalized Carlson iterating process approximation error

Hierarchical Polytope ARTMAP for Supervised Learning

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Journal of Computer Science & Technology 2010年第5期25卷 1071-1082页

作者：廖鑫鹏吴永强韩崇昭 Southwest Research Institute of Electronics and Telecommunication Technology College of Electronics and Information Engineering Xi'an Jiaotong University

The recent Polytope ARTMAP（PTAM） suggests that irregular polytopes are more flexible than the predefined category geometries to approximate the borders among the desired output ***,category expansion and adjustment steps without statistical information make PTAM not robust to noise and category *** order to push the learning problem towards Structural Risk Minimization（SRM）,this paper proposes Hierarchical Polytope ARTMAP （HPTAM） to use a hierarchical structure with different levels,which are determined by the complexity of regions incorporating the input ***,overlapping of simplexes from the same desired prediction is designed to reduce category *** HPTAM is still inevitably sensible to noisy outliers in the presence of noise,main experimental results show that HPTAM can achieve a balance between representation error and approximation error,which ameliorates the overall generalization capabilities.

关键词： structural risk minimization polytope ARTMAP hierarchical structure representation error approximation error

Estimating Subdivision Depth of Catmull-Clark Surfaces

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Journal of Computer Science & Technology 2004年第5期19卷 657-664页

作者： Hua-WeiWang Kai-HuaiQin DepartmentofComputerScienceandTechnology TsinghuaUniversityBeijing100083P.R.China

In this paper, both general and exponential bounds of the distance between a uniform Catmull-Clark surface and its control polyhedron are derived. The exponential bound is independent of the process of subdivision and can be evaluated without recursive subdivision. Based on the exponential bound, we can predict the depth of subdivision within a user-specified error tolerance. This is quite useful and important for pre-computing the subdivision depth of subdivision surfaces in many engineering applications such as surface/surface intersection, mesh generation, numerical control machining and surface rendering.

关键词： Catmull-Clark surface subdivision depth control polyhedron approximation error

On the approximation of an Analytic Function Represented by Laplace-Stieltjes Transformation

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Analysis in Theory and Applications 2015年第4期31卷 407-420页

作者： Chhaya Singhal G.S.Srivastava Department of Mathematics Jaypee Institute of Information Technology

In the present paper,we have considered the approximation of analytic functions represented by Laplace-Stieltjes transformations using sequence of definite integrals. We have characterized their order and type in terms of the rate of decrease of E;（F,β） where E;（F,β） is the error in approximating of the function F（s） by definite integral polynomials in the half plane Res≤β<α.

关键词： Laplace-Stieltjes transformation analytic function order type approximation error

A search-free near-field source localization method with exact signal model

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Journal of Systems Engineering and Electronics 2021年第4期32卷 756-763页

作者： PAN Jingjing SINGH Parth Raj MEN Shaoyang Key Laboratory of Dynamic Cognitive System of Electromagnetic Spectrum Space Nanjing University of Aeronautics and AstronauticsNanjing 211106China Department of Electronic Engineering Nanjing University of Aeronautics and AstronauticsNanjing 211106China International Electronics Engineering S.A. Bissen L-7795Luxembourg School of Medical Information Engineering Guangzhou University of Chinese MedicineGuangzhou 510006China

Most of the near-field source localization methods are developed with the approximated signal model,because the phases of the received near-field signal are highly ***,the approximated signal model based methods suffer from model mismatch and performance degradation while the exact signal model based estimation methods usually involve parameter searching or multiple decomposition *** this paper,a search-free near-field source localization method is proposed with the exact signal ***,the approximative estimates of the direction of arrival(DOA)and range are obtained by using the approximated signal model based method through parameter separation and polynomial rooting ***,the approximative estimates are corrected with the exact signal model according to the exact expressions of phase difference in near-field *** proposed method avoids spectral searching and parameter pairing and has enhanced estimation *** simulations are provided to demonstrate the effectiveness of the proposed method.

关键词： near-field source localization polynomial rooting approximation error exact signal model

Data-Based Optimal Tracking of Autonomous Nonlinear Switching Systems

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IEEE/CAA Journal of Automatica Sinica 2021年第1期8卷 227-238页

作者： Xiaofeng Li Lu Dong Changyin Sun the School of Automation Southeast UniversityNanjing 210096 the Key Laboratory of Measurement and Control of Complex Systems of Engineering Ministry of EducationSoutheast UniversityNanjing 210096China the College of Electronics and Information Engineering Tongji UniversityShanghai 201804China

In this paper,a data-based scheme is proposed to solve the optimal tracking problem of autonomous nonlinear switching *** system state is forced to track the reference signal by minimizing the performance ***,the problem is transformed to solve the corresponding Bellman optimality equation in terms of the Q-function(also named as action value function).Then,an iterative algorithm based on adaptive dynamic programming(ADP)is developed to find the optimal solution which is totally based on sampled *** linear-in-parameter(LIP)neural network is taken as the value function *** the presence of approximation error at each iteration step,the generated approximated value function sequence is proved to be boundedness around the exact optimal solution under some verifiable ***,the effect that the learning process will be terminated after a finite number of iterations is investigated in this paper.A sufficient condition for asymptotically stability of the tracking error is ***,the effectiveness of the algorithm is demonstrated with three simulation examples.

关键词： Adaptive dynamic programming approximation error data-based control Q-learning switching system

Lagrange插值在最大框架下的逼近误差

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高等学校计算数学学报 2017年第2期39卷 145-152页

作者：黄蓉武文艳天津师范大学数学科学学院

1引言代数多项式插值理论是函数逼近理论和计算数学的重要研究内容.在函数逼近理论研究中,传统研究内容是对个体函数讨论插值多项式依赖于连续模或多项式最佳逼近的误差估计问题,其系列研究结果可见专著[7]或综述文章[8],近期研究结果可... 详细信息

1引言代数多项式插值理论是函数逼近理论和计算数学的重要研究内容.在函数逼近理论研究中,传统研究内容是对个体函数讨论插值多项式依赖于连续模或多项式最佳逼近的误差估计问题,其系列研究结果可见专著[7]或综述文章[8],近期研究结果可见[1,5]及

关键词： Lagrange interpolation worst case setting approximation error analytic function class

Estimation of the Misclassification error for Multicategory Support Vector Machine Classification

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Acta Mathematica Sinica,English Series 2008年第3期24卷 511-528页

作者： Bing Zheng LI Department of Mathematics Zhejiang University Hangzhou 310028 P. R. China

The purpose of this paper is to provide an error analysis for the multicategory support vector machine （MSVM） classificaton problems. We establish the uniform convergency approach for MSVMs and estimate the misclassification error. The main difficulty we overcome here is to bound the offset vector. As a result, we confirm that the MSVM classification algorithm with polynomial kernels is always efficient when the degree of the kernel polynomial is large enough. Finally the rate of convergence and examples are given to demonstrate the main results.

关键词： multicategory support vector machine classifier misclassification error reproducing kernel Hilbert space approximation error