纤维丛上一般非线性控制系统的几何框架及其最小实现理论<sup>*</sup>

慕小武

纤维丛上一般非线性控制系统的几何框架及其最小实现理论^*

慕小武

郑州大学系统科学与数学系, 郑州 450052

基金项目: * 国家自然科学青年基金,河南省自然科学资金

计量
- 文章访问数: 2128
- HTML全文浏览量: 132
- PDF下载量: 461
- 被引次数: 0
出版历程
- 收稿日期: 1996-03-20
- 刊出日期: 1996-10-15

Geometric Framework and Minimal Realizations of Nonlinear Systems on Fibre Bundle

Mu Xiaowu

Department of Mathematics, Zhengzhou University, Zhengzhou 450052, P. R. China

摘要

摘要: 本文探讨正确建立一般非线性控制系统纤维丛框架的途径,并研究了纤维丛上系统的最小实现理论。我们在本文中通过引进(F,φ)同构,(F,φ)同态,强等价等新概念,实质上拓广了H.J.Sussmann所发展的非线性系统实现理论的经典概念和结果,并证明了纤维丛上的一般非线性系统的最小实现唯一性定理。
- 纤维丛 /
- 能观性 /
- 能控性 /
- 最小实现
Abstract: The definition of nonlinear control sysms on fibre bundles proposed by Brockett and Willems is incomplete from the mathematical view geometric framework is proposed and a minimal realization theory is developed for nonlinear control systems on fibre bundles which is elaborated as a natural generalization of Sussmann's theory and differs essentially from Van der Schaft's approach. Limitations of realization theory given by Van der Schaft are also discussed.
- fibre bundle /
- controllability /
- observability /
- minimality

HTML全文

参考文献(16)

[1]	R.W, Brockett, Control Theory and Analytical Mechanics,Geometrical Control Theory, Ed, by C. Martin and R, Hermann, Math, Sci, Press (1977).
[2]	R.W, Brockett, Nonlinear control theory and differential geometry,Proceeding of the International Congress of Mathematicans, August 16-24, 1983,Warszawa(1983).
[3]	H, Nijmeijer and A,J.Van der Schaft, Nonlinear Dynamical Control Systems,Springer-Verlag(1990).
[4]	J.C, Willems, Systems theoretic models for the analysis of physical systems,Ricerche di Automatics (special issue on systems),10(2)(1979).
[5]	A,J.Van der Schaft,System theoretic descriptions of physical systems, Doct.Dissertation, University of Groningen(1983).
[6]	H, Nijimeijer and A. T.Van dcr Schaft, Controlled invariance for nonlinear systems, IEEE Trans.Auto,Control, AC-27(4)(1982).
[7]	H, Nijimeijer, On the theory of nonlinear control systems, Lectures Notes in Control&Informetions, (135), Springer-Verlag(1989).
[8]	A,J.Van der Schaft,Controllability a,nd observability.for aftinc nonlinear Hamiltonian systems,IEEE Trans, Auto, Control, AC-27 (1982), 490-492.
[9]	H,J.Sussmann.E} is fence&uniqueness of minimal relizations of nonlinear systems,Math,Sys,Theory, 10(1977),263-284.
[10]	H,J, Sussmann, Orbits of families of vector fields and integrability of distributions,Trans.Amer, Math, Society, 180 (1973), 171-188.
[11]	R, Hermann and A, T, Krener, Nonlinear controllability and observability,IEEE,Traus,Auto,Control,AC-22(5) (1977).
[12]	H,J.Sussmann, Lie brackets,real analyticity and geometric control,Progress in Math.,Differential Geometric Control Theory, MA Birkhauser (1983).
[13]	H.J. Sussmann and V. Jurdjevic, Controllability of nonlinear systems, J.Diff.Equ.,12 (1972).
[14]	慕小武,一般非线性控制系统和力学控制系统的统一纤维丛框架及其实现理论,北京大学博士学位论文(1991).
[15]	A, Isidori,Nonlinear Control Systems, 2nd ed. Springer-Yerlag(1989).
[16]	慕小武,纤维丛上一般非线性系统的能观性与能控性,《中国控制会议论文集》,科学出版社(1995).