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

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Abstract

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 Sun Yimin and Guo Lei recently. Furthermore, we will give two examples to illustrate its application.

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References

  1. Isidori A. Nonlinear Control Systems. 3rd ed. London: Springer-Verlag, 1995

    MATH  Google Scholar 

  2. Jurdjevic V, Geometric Control Theory. New York: Cambridge University Press, 1997

    MATH  Google Scholar 

  3. Casti J L. Nonlinear System Theory. Orlando: Academic Press, Inc. Ltd., 1985

    MATH  Google Scholar 

  4. Nijmeijer H. van der Schaft A. Nonlinear Dynamical Control Systems. New York: Springer-Verlag, 1990

    MATH  Google Scholar 

  5. Sontag E D. Mathematical Control Theory—Deterministic Finite Dimensional Systems. New York: Springer-Verlag, 1998

    MATH  Google Scholar 

  6. Sussmann H J, Jurdjevic V. Controllability of nonlinear systems. J Diff Eqns, 1972, 12(1): 95–116

    Article  MATH  MathSciNet  Google Scholar 

  7. Brockett R W. System theory on group manifolds and coset spaces. SIAM J Contr, 1972, 10: 265–284

    Article  MATH  MathSciNet  Google Scholar 

  8. Hunt L R. Global controllability of nonlinear systems in two dimensions. Math Syst Theory, 1980, 13: 361–376

    Article  MATH  Google Scholar 

  9. Hermes H. On local and global controllability, SIAM J Cotrol, 12(2): 1974, 252–261

    Article  MATH  MathSciNet  Google Scholar 

  10. Aeyels D. Local and gobal controllability for nonlinear systems. Syst Contr Lett, 1984, 5: 19–26

    Article  MATH  MathSciNet  Google Scholar 

  11. Kaya C Y, Noakes J L. Closed trajectories and global controllability in the plane. IMA J math Contr Inf, 1997, 14: 353–369

    Article  MATH  MathSciNet  Google Scholar 

  12. Cheng D. Controllability of switched bilinear systems. IEEE Trans Automat Contr, 2005, 50(4): 511–515

    Article  Google Scholar 

  13. Caines P E, Lemch E S. On the global controllability of nonlinear systems: Fountains, recurrence, and applications to hamiltonian systems. SIAM J Control Optim, 2003, 41(5): 1532–1553

    Article  MATH  MathSciNet  Google Scholar 

  14. Nikitin S. Global Controllability and Stabilization of Nonlinear Systems. Singapore: World Scientific Publishing Co. Pte. Ltd, 1994

    MATH  Google Scholar 

  15. Sun Y M. Necessary and sufficient condition for global controllability of planar affine nonlinear systems. IEEE Trans Automat Contr, 2007, 52(8): 1454–1460

    Article  Google Scholar 

  16. Sun Y M, Guo L. On global controllability of planar affine nonlinear systems. In: Proceedings of the 24th Chinese Control Conference, Guangzhou: South China University of Technology Press, 2005. 1765–1769

    Google Scholar 

  17. Khalil H K. Nonlinear Systems. 2nd ed. Upper Saddle River, NJ: Prentice-Hall, 1996

    Google Scholar 

  18. Arnold V I. Ordinary Differential Equations. (Silverman R A, trans. ed.), Cambridge: MIT Press, 1973

    MATH  Google Scholar 

  19. Whitney H. Analytic extensions of differentiable functions defined in closed sets. Trans Amer Math Soc, 1934, 34: 63–89

    Article  MathSciNet  Google Scholar 

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Authors and Affiliations

  1. Department of Electrical Engineering, Tsinghua University, Beijing, 100084, China

    Sun YiMin, Mei ShengWei & Lu Qiang

Authors
  1. Sun YiMin
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  2. Mei ShengWei
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  3. Lu Qiang
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Corresponding author

Correspondence to Sun YiMin.

Additional information

Supported by the National Natural Science Foundation of China (Grant Nos. 50525721, 60221301 and 60334040) and China Postdoctoral Science Foundation

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Sun, Y., Mei, S. & Lu, Q. On global controllability of affine nonlinear systems with a triangular-like structure. Sci. China Ser. F-Inf. Sci. 50, 831–845 (2007). https://doi.org/10.1007/s11432-007-0058-x

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  • DOI: https://doi.org/10.1007/s11432-007-0058-x

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