不变流形方法与非线性控制系统的能控制性

The Invariant Manifold Method and the Controllability of Nonlinear Control System

Department of Chemical Processing Machinery, Sichuan University, Chengdu 610065, P R China

摘要: 在Kovalev方法基础上运用不变流形研究非线性系统的能控制性问题,得出了一类仿射非线性系统能控的必要条件,讨论了必要条件的实现问题,研究了带有两个陀螺的刚体运动,证明了它满足能控性的必要条件.
- 非线性控制系统 /
- 能控性 /
- 有向流形 /
- 不变流形 /
- 基系统 /
- 刚体动力学系统
Abstract: The problem of controllability of nonlinear control system is a significant field which has an extensive prospect of application.A.M.Kovalev of Ukraine Academy of Science applied the oriented manifold method developed in dynamics of rigid body to nonlinear control system for the first time and obtained a series of efficient results.Based on Kovalev.s oriented manifold method,firstly,by invariant manifold method the problem of controllability of nonlinear control system was studied and the necessary condition of the controllability of a kind of affine nonlinear system was given out.Then the realization of the necessary condition was discussed.At last,the motion of a rigid body with two rotors was investigated and the necessary condition which is satisfied by this system was proved.
- nonlinear control system /
- controllability /
- oriented manifold /
- invariant manifold /
- basic system /
- dynamics of rigid body

[1]	Isidori A.Nonlinear Control Systems,An Introduction[M].Vol 72.Berlin:Springer-Verlag,1985.
[2]	程代展.非线性系统的几何理论[M].北京:科学出版社,1988.
[3]	程代展,等.非线性系统研究动态与展望[J].控制与决策,1991,6(5):394) 400.
[4]	Hermann R,Krener A J.Nonlinear controllability and observability[J].IEEE Tran sactions Automatic Control,1977,AC-22(5):728-740.
[5]	Sussmann H J,Jurdjevic V.Controllability of nonlinear systems[J].J Differ ential Equations,1972,12(3):313-329.
[6]	Sussmann H J.A general theorem on local controllability[J].SIAM J Contr & Opt,1987,25(1):158-194.
[7]	Cao L,Zheng Y F.Some toplogical properties of reachable semigroup of the systems on Lie group[A].In:C I Byrnes,et al Eds.Analysis and Contr ol of Nonlinear Sy stems[C].Amsterdam:North-Holland,1988,149-154.