Structural Conditions on Observability of Nonlinear Systems

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In this paper parameter space and Lebesgue measurement are introduced into analysis of nonlinear systems. Structural observability rank condition is defined and together with the distinguishabililty the structural observability criterions of nonlinear systems are obtained. It proves that when the parameters are not identifiable the solutions with the same time but different parameters are also indistinguishable. Differential geometry and algebraic methods are used to investigate the observability problem, and it is proved that there are some relations between these two methods. Finally, examples are used to illustrate applications of the structural observability criterions.

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Structural observability, identifiability, nonlinear systems, parameter space

Короткий адрес: https://sciup.org/15011630

IDR: 15011630

Список литературы Structural Conditions on Observability of Nonlinear Systems

  • H. W. Knobloch, “Observability of nonlinear systems”, MATHEMATICA BOHEMICA, No. 4, pp. 411-418, 2006.
  • M. Hwang and J. H. Seinfeld, “Observability of Nonlinear Systems”, Journal of Optimization Theory and Applications, Vol. 10, No. 2, pp. 67-77, 1972.
  • R. Hermann and A. Krener, “Nonlinear controllability and observability”, IEEE Trans. AC-22, pp. 728-740, 1977.
  • Z. Bartosiewicz, “Local observability of nonlinear systems,” Systems & Control Letters 25, pp. 295-298, 1995.
  • K.S. Lu and J.N. Wei, “Rational function matrices and structural controllability and observability”. IEE Proceedings-D. 138, pp. 388-394, 1991.
  • K.S. Lu and J.N. Wei, “Reducibility condition of a class of rational function matrices”, SIAM J Matrix Anal Appl. 15, pp. 151-161, 1994.
  • K.S. LU and K. LU, “Controllability and observability criteria of RLC networks over F(z)”, International Journal of Circuit Theory and Applications, 29, pp. 337-341, 2001.
  • Kai-Sheng Lu, Guo-Zhang etc., “Various sufficient conditions of separability, reducibility, controllability and observability for electrical networks over F(z)”, IEEE Proceedings of Sixth International Conference on Machine Learning Cybernetics, (5), pp. 2784-2790, 2007.
  • Sette Diop and Michel Fliess, “Nonlinear observability, identifiability, and persistent trajectories”, Proc. of the 30th CDC, pp. 714-719, 1991
  • K. E. Starkov, “Observability of smooth control systems”, Journal of Mathematical Sciences, VoL 78, No. 4, pp. 433-496, February 1996.
  • K.S. Lu and G.Z. Gao, “The Node Voltage Equations and Structural Conditions of Observability for RLC Networks over F(z)”, Proc of IEEE ISCAS, pp. 764-767, 2005.
  • G. Conte, C.H. Moog and A.M. Perdon, Algebraic Methods for Nonlinear Control Systems. Theory and Applications, 2nd ed., Springer, 2007.
  • Kaisheng Lu, Rational function systems and electric networks in multi-parameters. Beijing: Science press, 2010 (in Chinese).
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