A Simple Sufficient Criterion of the Global Controllability for a Class of Planar Polynomial Systems
详细信息 查看官网全文
- 英文论文题名：A Simple Sufficient Criterion of the Global Controllability for a Class of Planar Polynomial Systems
- 论文作者：Yimin SUN ; Weichen XIE
- 英文论文作者：Yimin SUN ; Weichen XIE ; School of Mathematics ; Sun Yat-sen University
- 年：2017
- 作者机构：School of Mathematics,Sun Yat-sen University;
- 英文论文关键词：Polynomial ; global controllability ; sufficient criterion algorithm ; degree ; mathematics mechanization method
- 会议召开时间：2017-07-26
- 会议录名称：第36届中国控制会议论文集（A）
- 英文会议录名称：Proceedings of the 36th Chinese Control Conference（A）
- 语种：英文
- 分类号：O231
- 学会代码：KZLL
- 会议名称：第36届中国控制会议
- 会议地点：中国辽宁大连
- 主办单位：中国自动化学会控制理论专业委员会
- 学会名称：中国自动化学会控制理论专业委员会
- 页数：4
- 文件大小：175k
- 原文格式：D
- 会议级别：全国
摘要
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.
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.
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.
引文
[1]D.Aeyels.Local and global controllability for nonlinear systems.Systems&Control Letters,5:19–26,1984.
[2]S.V.Emel’yanov,S.K.Korovin,and S.V.Nikitin.Controllability of nonlinear systems and systems on a foliation.Sov.Phys.Dokl.,33(3):167–169,1988.
[3]Y.M.Sun.Necessary and sufficient condition for global controllability of planar affine nonlinear systems.IEEE Trans.Automat.Contr.,52(8):1454–1460,2007.
[4]Y.M.Sun.On the global controllability for a class of 3-dimensional nonlinear systems with two inputs.Proceedings of the 35th Chinese Control Conference,941–944,2016.
[5]S.Basu,R.Pollack,and M.F.Roy.Algorithms in Real Algebraic Geometry.Springer-Verlag,Heidelberg,second edition,2006.
[6]L.Yang,X.Hou,and Z.Zeng.A complete discriminant system for polynomials.Science in China,Ser.E,39(6):628–646,1996.
[7]Q.Q.Li,X.L.Xu,and Y.M.Sun.A constructive criterion algorithm of the global controllability for a class of planar polynomial systems.IET Control Theory and Applications,9(5):811–816,2015.
[8]X.L.Xu,Q.Q.Li,and Y.M.Sun.Application of sturm theorem in the global controllability of a class of high dimensional polynomial systems.Journal of Systems Science and Complexity,28(5):1049–1057,2015.
[9]V.Jurdjevic.Geometric Control Theory.Cambridge University Press,New York,1997.
[10]J.W.Milnor.Topology from the differentiable viewpoint.Post&Telecom Press,Beijing,2008.
[11]H.Eschrig.Topology and Geometry for Physics.Peking University Press,Beijing,2014.
[12]D.M.Wang,C.Q.Mou,X.L.Li,J.Yang,Y.Jin,and Y.L.Huang.Polynomial Algebra.Higher Education Press,Beijing,2011(In Chinese).
[13]E.A.Coddington and N.Levinson.Theory of Ordinary Differential Equations.Mc Graw-Hill,New York,1955.
[2]S.V.Emel’yanov,S.K.Korovin,and S.V.Nikitin.Controllability of nonlinear systems and systems on a foliation.Sov.Phys.Dokl.,33(3):167–169,1988.
[3]Y.M.Sun.Necessary and sufficient condition for global controllability of planar affine nonlinear systems.IEEE Trans.Automat.Contr.,52(8):1454–1460,2007.
[4]Y.M.Sun.On the global controllability for a class of 3-dimensional nonlinear systems with two inputs.Proceedings of the 35th Chinese Control Conference,941–944,2016.
[5]S.Basu,R.Pollack,and M.F.Roy.Algorithms in Real Algebraic Geometry.Springer-Verlag,Heidelberg,second edition,2006.
[6]L.Yang,X.Hou,and Z.Zeng.A complete discriminant system for polynomials.Science in China,Ser.E,39(6):628–646,1996.
[7]Q.Q.Li,X.L.Xu,and Y.M.Sun.A constructive criterion algorithm of the global controllability for a class of planar polynomial systems.IET Control Theory and Applications,9(5):811–816,2015.
[8]X.L.Xu,Q.Q.Li,and Y.M.Sun.Application of sturm theorem in the global controllability of a class of high dimensional polynomial systems.Journal of Systems Science and Complexity,28(5):1049–1057,2015.
[9]V.Jurdjevic.Geometric Control Theory.Cambridge University Press,New York,1997.
[10]J.W.Milnor.Topology from the differentiable viewpoint.Post&Telecom Press,Beijing,2008.
[11]H.Eschrig.Topology and Geometry for Physics.Peking University Press,Beijing,2014.
[12]D.M.Wang,C.Q.Mou,X.L.Li,J.Yang,Y.Jin,and Y.L.Huang.Polynomial Algebra.Higher Education Press,Beijing,2011(In Chinese).
[13]E.A.Coddington and N.Levinson.Theory of Ordinary Differential Equations.Mc Graw-Hill,New York,1955.