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Application of Sturm Theorem in the global controllability of a Class of High Dimensional Polynomial Systems

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Journal of Systems Science & Complexity 2015年第5期28卷 1049-1057页

作者： XU Xueli LI Qianqian SUN Yimin Guangdong Province Key Laboratory of Computational Science School of Mathematics and Computational Science Sun Yat-Sen University

In this paper, the global controllability for a class of high dimensional polynomial systems has been investigated and a constructive algebraic criterion algorithm for their global controllability has been obtained. By the criterion algorithm, the global controllability can be determined in finite steps of arithmetic operations. The algorithm is imposed on the coefficients of the polynomials only and the analysis technique is based on Sturm Theorem in real algebraic geometry and its modern ***, the authors will give some examples to show the application of our results.

关键词： global controllability high dimensional systems number of sign variations polynomial Sturm theorem.

On global controllability of affine nonlinear systems with a triangular-like structure

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Science in China(Series F) 2007年第6期50卷 831-845页

作者： SUN YiMin MEI ShengWe LU Qiang Department of Electrical Engineering Tsinghua University Beijing 100084 China

In this paper, we investigate a class of affine nonlinear systems with a triangular-like structure and present its necessary and sufficient condition for global controllability, by using the techniques developed by Su... 详细信息

关键词： affine nonlinear systems global controllability vector field

On global controllability for a class of polynomial affine nonlinear systems

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控制理论与应用（英文版） 2012年第3期10卷 332-336页

作者： Yimin SUN Guangdong Province Key Laboratory of Computational Science School of Mathematics and Computational Science Sun Yat-sen University Guangzhou Guangdong 510275 China

In this paper, a necessary and sufficient condition of the global controllability for a class of low dimensional polynomial affine nonlinear systems with special structure is obtained. The condition is imposed on the coefficients of the system only and the methods are based on Green＇s formula and the trajectory analysis of planar linear system. Furthermore, I point out that the global controllability does not hold for the corresponding high dimensional polynomial system.

关键词： Affine nonlinearity Polynomial system global controllability Green's Formula

A Simple Sufficient Criterion of the global controllability for a Class of Planar Polynomial Systems

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A Simple Sufficient Criterion of the Global Controllability ...

第36届中国控制会议

作者： Yimin SUN Weichen XIE School of Mathematics Sun Yat-sen University

ISBN: (纸本)9781538629185

Since the global controllability of planar nonlinear systems was completely solved and the necessary and sufficient condition was obtained, it has been certainly worth finding a feasible algorithm to check up on the condition. However, the condition is too complicated to be verified generally, which limits its application largely. This paper will investigate a sufficient condition with less computational complexity for the global controllability of planar polynomial systems. Based on the degree of criterion function of planar systems on control curves and mathematics mechanization method, we present a simple sufficient criterion algorithm for the global controllability of a class of planar polynomial systems. All conditions are imposed on the structure of the system only. Finally, we give some examples to show the application of our results.

关键词： Polynomial global controllability sufficient criterion algorithm degree mathematics mechanization method

Application of Sturm Theorem in the global controllability of a Class of High Dimensional Polynomial Systems

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Journal of Systems Engineering and Electronics 2015年第5期26卷 1049-1057页

作者： XU Xueli LI Qianqian SUN Yimin Guangdong Province Key Laboratory of Computational Science School of Mathematics and Computational Science Sun Yat-Sen University

In this paper, the global controllability for a class of high dimensional polynomial systems has been investigated and a constructive algebraic criterion algorithm for their global controllability has been obtained. By the criterion algorithm, the global controllability can be determined in finite steps of arithmetic operations. The algorithm is imposed on the coefficients of the polynomials only and the analysis technique is based on Sturm Theorem in real algebraic geometry and its modern progress. Finally, the authors will give some examples to show the application of our results.

关键词： global controllability high dimensional systems number of sign variations polynomial,Sturm theorem.

global controllability for a Class of 4-dimensional Affine Nonlinear Systems

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Global Controllability for a Class of 4-dimensional Affine N...

第三十届中国控制会议

作者： SUN Yimin School of Mathematics and Computational Science,Sun Yat-sen University,Guangzhou,510275,P.R.China

＜正＞This paper will investigate and present a necessary and sufficient condition of the global controllability for a class of 4-dimensional affine nonlinear system with special *** condition is imposed on the coefficients of the system only. The methods are based on Green’s formula and the trajectory analysis of planar linear system.

关键词： Afflne nonlinearity 4-dimensional system global controllability Green’s Formula

global controllability of a Class of 3-dimensional Affine Nonlinear Systems

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Global Controllability of a Class of 3-dimensional Affine No...

第二十九届中国控制会议

作者： SUN Yimin School of Mathematics and Computational Science,Sun Yat-sen University,Guangzhou 510275,P.R.China.

In this paper,we will consider the global controllability for a class of 3-dimensional affine nonlinear systems.A necessary and sufficient condition for their global controllability is *** method is mainly based on Gr... 详细信息

关键词： Affine Nonlinearity Three Dimensional System global controllability Green’s Formula.

Further Results on global controllability of Affine Nonlinear Systems

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Further Results on Global Controllability of Affine Nonlinea...

第25届中国控制会议

作者： Sun Yimin ,Guo Lei,Lu Qiang ,Mei Shengwei Department of Electrical Engineering,Tsinghua University,Beijing 100084 Academy of Mathematics and Systems Science,Chinese Academy of Sciences,Beijing 100080

＜正＞Most of the existing results on controllability of nonlinear systems are concerned with local controllability. In this paper,we will present some further results on global controllability of two classes of affine nonlinear systems,by using the techniques developed recently in [1][2]. The first class is planar affine nonlinear systems with one singular point,the second class is high-dimensional affine nonlinear systems with special structure.

关键词： Nonlinear systems global controllability vector field

On global controllability of Planar Affine Nonlinear Systems

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On Global Controllability of Planar Affine Nonlinear Systems

第二十四届中国控制会议

作者： Yimin Sun, Lei Guo Academy of Mathematics and Systems Science, Chinese Academy of Sciences

＜正＞ Most of the existing results on controllability of nonlinear systems are concerned with local controllability. In this paper, we will investigate the global controllability of general planar affine nonlinear systems with single-input. By using a new method, we find the necessary and sufficient condition for global controllability and globally asymptotic controllability respectively. Our analysis is based on some basic facts in planar topology and in the geometric theory of ordinary differential equations.

关键词： Affine nonlinear systems global controllability vector field Jordan Theorem control curve