Computer Algorithms of Pseudo‐Formal Linearization Based on Chebyshev Interpolation for Nonlinear Time‐Varying Systems and a Nonlinear Filter

In this paper, we design algorithms of a linearization and a nonlinear filter for time‐varying systems using a pseudo‐formal linearization based on Chebyshev interpolation. Presented algorithms make it easy to linearize nonlinear time‐varying systems and to synthesize a nonlinear filter. They can al...

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Vydáno v:IEEJ transactions on electrical and electronic engineering
Hlavní autoři: Komatsu, Kazuo, Takata, Hitoshi
Médium: Journal Article
Jazyk:angličtina
Vydáno: 29.07.2025
ISSN:1931-4973, 1931-4981
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Abstract In this paper, we design algorithms of a linearization and a nonlinear filter for time‐varying systems using a pseudo‐formal linearization based on Chebyshev interpolation. Presented algorithms make it easy to linearize nonlinear time‐varying systems and to synthesize a nonlinear filter. They can also reduce the computational burden in both linearization and estimation processes by exploiting Chebyshev interpolation. This algorithm applies a Kalman filter to each linearized system, which is obtained in a some subdomain by using pseudo‐formal linearization, to construct a nonlinear filter that is valid for the entire domain. We demonstrate the effectiveness of algorithms through demonstrating numerical experiments with linearizations and a nonlinear filter of an academic bioreactor. © 2025 Institute of Electrical Engineers of Japan and Wiley Periodicals LLC.
AbstractList In this paper, we design algorithms of a linearization and a nonlinear filter for time‐varying systems using a pseudo‐formal linearization based on Chebyshev interpolation. Presented algorithms make it easy to linearize nonlinear time‐varying systems and to synthesize a nonlinear filter. They can also reduce the computational burden in both linearization and estimation processes by exploiting Chebyshev interpolation. This algorithm applies a Kalman filter to each linearized system, which is obtained in a some subdomain by using pseudo‐formal linearization, to construct a nonlinear filter that is valid for the entire domain. We demonstrate the effectiveness of algorithms through demonstrating numerical experiments with linearizations and a nonlinear filter of an academic bioreactor. © 2025 Institute of Electrical Engineers of Japan and Wiley Periodicals LLC.
Author Takata, Hitoshi
Komatsu, Kazuo
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  organization: Kagoshima University 1–21–40 Korimoto Kagoshima 890‐0065 Japan
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