Formal Linearization of Nonlinear Time-Varying Dynamic Systems using Chebyshev and Laguerre Polynomials
| Authors: | Takata Hitoshi, Kagoshima University, Japan
Komatsu Kazuo, Kumamoto National College of Technology, Japan
Sano Hideki, Kagoshima University, Japan |
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| Topic: | 1.1 Modelling, Identification & Signal Processing |
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| Session: | Nonlinear Filtering |
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| Keywords: | Nonlinear system, Linearization, Time-varying system, Polynomial transforms, Observers |
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Abstract
This paper is concerned with a formal linearization problem for a general class of nonlinear time-varying dynamic systems. To a given system, a linearization function is made up of Chebyshev polynomials about its state variables. The nonlinear time-varying system is transformed into a linear time-varying system in terms of the linearization function using Chebyshev interpolation to state variables and Laguerre expansion to time variable. An error bound formula of this linearization which is derived in this paper explains that the accuracy of this algorithm is improved as the order of Chebyshev and Laguerre polynomials increases. As its application, a nonlinear observer is designed to demonstrate the usefulness of this formal linearization approach.
