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Conformable fractional-order fixed-point state estimator for discrete-time nonlinear systems

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  • Oliva-Gonzalez, Lorenz Josue
  • Martínez-Guerra, Rafael

Abstract

This paper presents an approach to deal with the state estimation problem in discrete-time nonlinear systems. The approach translates the state estimation problem into a root-finding problem; hence, a state estimator based on a numerical method is designed. In particular, we consider a modification of the conformable fractional-order vector Newton–Raphson method. This fractional-order numerical method has been introduced recently and presents remarkable properties compared to its integer-order version. For instance, it exhibits low computational cost, fewer iterations to achieve convergence, and mitigates divergence problems. Therefore, the proposed state estimator inherits these properties, making it an attractive alternative. On the other hand, the convergence of the state estimator is analyzed using an extension of the Banach fixed-point theorem, providing convergence conditions. Eventually, several numerical simulations are performed to evaluate the proposed approach.

Suggested Citation

  • Oliva-Gonzalez, Lorenz Josue & Martínez-Guerra, Rafael, 2025. "Conformable fractional-order fixed-point state estimator for discrete-time nonlinear systems," Chaos, Solitons & Fractals, Elsevier, vol. 199(P3).
    • Handle: RePEc:eee:chsofr:v:199:y:2025:i:p3:s0960077925008380
    DOI: 10.1016/j.chaos.2025.116825
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    References listed on IDEAS

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    1. Giro Candelario & Alicia Cordero & Juan R. Torregrosa, 2020. "Multipoint Fractional Iterative Methods with (2 α + 1)th-Order of Convergence for Solving Nonlinear Problems," Mathematics, MDPI, vol. 8(3), pages 1-15, March.
    2. Vargas Alvarez, Hector & Fabiani, Gianluca & Kazantzis, Nikolaos & Kevrekidis, Ioannis G. & Siettos, Constantinos, 2024. "Nonlinear discrete-time observers with Physics-Informed Neural Networks," Chaos, Solitons & Fractals, Elsevier, vol. 186(C).
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