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The invariant manifold method and the controllability of nonlinear control system

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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.

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References

  1. Isidori A.Nonlinear Control Systems, An Introduction[M]. Vol72, Berlin: Springer-Verlag, 1985.

    Google Scholar 

  2. CHEN Dai-zhan.Geometry Theory of Nonlinear System[M]. Beijing: Science Press, 1988. (in Chinese)

    Google Scholar 

  3. CHEN Dai-zhan, et al. The researching tendency and prospect of nonlinear system[J].J Control & Decision, 1991,6(5):394–400. (in Chinese)

    Google Scholar 

  4. Hermann R, Krener A J. Nonlinear controllability and observability[J].IEEE Transactions Automatic Control, 1977, AC-22(5):728–740.

    Article  MATH  MathSciNet  Google Scholar 

  5. Sussmann H J, Jurdjevic V. Controllability of nonlinear systems [J].J Differential Equations, 1972,12(3):313–329.

    MATH  MathSciNet  Google Scholar 

  6. Sussmann H J. A general theorem on local controllability[J].SIAM J Contr & Opt, 1987,25(1): 158–194.

    Article  MATH  MathSciNet  Google Scholar 

  7. Cao L, Zheng Y F. Some toplogical properties of reachable semigroup of the systems on Lie group [A]. In: C I Bynes, et al Eds.Analysis and Control of Nonlinear Systems[C]. Amsterdam: North-Holland, 1988, 149–154.

    Google Scholar 

  8. Cememov V N. The dynamic control system of sliding manifold[A]. In:Control Theory and Calculation[C]. Moscow: Science & Technology Press, 1976,31. (in Russian)

    Google Scholar 

  9. Kovalev A M.The Controllability, Observability and Coherence of Control System[M]. Kiev: Science Research, 1993. (in Russian)

    Google Scholar 

  10. Harlamov P V. The invariant relation system of differential equation[J].Solid Kinetics, 1974,6: 15–24. (in Russian)

    MATH  Google Scholar 

  11. Kovalev A M.The Nonlinear Control System Problems in Observation of Dynamic System Theory[M]. Kiev: Science Research, 1980. (in Russian)

    Google Scholar 

  12. Levi-Chivida T, Amaledge Y.Theoretic Mechanics[M], Vol2, Moscow: 1951. (in Russian)

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Authors and Affiliations

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

    Yang Liu Doctor

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  1. Yang Liu Doctor
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Communicated by YE Qing-kai

Bigraphy: YANG Liu(1971-)

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Liu, Y. The invariant manifold method and the controllability of nonlinear control system. Appl Math Mech 21, 1320–1330 (2000). https://doi.org/10.1007/BF02459255

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  • DOI: https://doi.org/10.1007/BF02459255

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