Commenced in January 2007
Frequency: Monthly
Edition: International
Paper Count: 30850
Design of Nonlinear Observer by Using Chebyshev Interpolation based on Formal Linearization

Authors: Kazuo Komatsu, Hitoshi Takata


This paper discusses a design of nonlinear observer by a formal linearization method using an application of Chebyshev Interpolation in order to facilitate processes for synthesizing a nonlinear observer and to improve the precision of linearization. A dynamic nonlinear system is linearized with respect to a linearization function, and a measurement equation is transformed into an augmented linear one by the formal linearization method which is based on Chebyshev interpolation. To the linearized system, a linear estimation theory is applied and a nonlinear observer is derived. To show effectiveness of the observer design, numerical experiments are illustrated and they indicate that the design shows remarkable performances for nonlinear systems.

Keywords: Nonlinear System, nonlinear observer, formal linearization, Chebyshev interpolation

Digital Object Identifier (DOI):

Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1223


[1] A. J. Krener, "Approximate Linearization by State Feedback and Coordinate Change," Systems and Control Letters, Vol.5, pp.181-185, 1984.
[2] R. Marino, "On the Largest Feedback Linearizable Subsystem," Systems and Control Letters, Vol.6, pp.345-351, 1986.
[3] W. T. Baumann and W. J. Rugh, "Feedback Control of Nonlinear Systems by Extended Linearization," IEEE Trans., AC-31, 1, pp.40-46, 1986.
[4] R. R. Kadiyala, "A Tool Box for Approximate Linearization on Nonlinear Systems," IEEE Control Systems, Vol.13, No.2, pp.47-57, 1993.
[5] A. Ishidori, Nonlinear Control Systems II , Springer-Verlag, London, 1999.
[6] H. K. Khalil, Nonlinear Systems, 3rd ed., New Jersey: Prentice Hall, 2002.
[7] H. Takata," Transformation of a Nonlinear System into an Augmented Linear System," IEEE Trans. on Automatic Control, Vol.AC-24, No.5, pp.736-741, 1979.
[8] H. Takata, K. Komatsu and H. Sano," Formal Linearization of Nonlinear Time-Varying Dynamic Systems Using Chebyshev and Laguerre Polynomials," Proc. of the 16th IFAC World Congress, pp.1-6, 2005.
[9] K. Komatsu and H. Takata,"Design of Nonlinear Observer by Using Augmented Linear System based on Formal Linearization of Polynomial Type," Proc. of World Academy of Science, Engineering and Technology, pp.29-32, 2009.
[10] K. Komatsu and H. Takata, "On a Nonlinear Observer via Formal Linearization based on Chebyshev Expansion," Proc. of 2010 RISP International Workshop on Nonlinear Circuits, Communications and Signal Processing, Hawaii, pp.576-579, 2010.
[11] G. W. Johnson, "A Deterministic Theory of Estimation and Control," IEEE Trans. on Automatic Control, pp. 380-384, 1969.
[12] A. P. Sage and C. C. White III, Optimum Systems Control, 2nd ed., Prentice-Hall,Inc., 1977.