Finite-Time Control Design for the Discrete-Time Chaotic Logistic Equation

Leonardo Acho; Pablo Buenestado; Gisela Pujol

doi:10.20944/preprints202407.0459.v1

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preprints.org > computer science and mathematics > applied mathematics > doi: 10.20944/preprints202407.0459.v1 (registering DOI)

Preprint Article Version 1 This version is not peer-reviewed

Finite-Time Control Design for the Discrete-Time Chaotic Logistic Equation

Leonardo Acho

^* ,

Pablo Buenestado

Gisela Pujol

Version 1 : Received: 4 July 2024 / Approved: 4 July 2024 / Online: 5 July 2024 (02:50:00 CEST)

How to cite: Acho, L.; Buenestado, P.; Pujol, G. Finite-Time Control Design for the Discrete-Time Chaotic Logistic Equation. Preprints 2024, 2024070459. https://doi.org/10.20944/preprints202407.0459.v1 Acho, L.; Buenestado, P.; Pujol, G. Finite-Time Control Design for the Discrete-Time Chaotic Logistic Equation. Preprints 2024, 2024070459. https://doi.org/10.20944/preprints202407.0459.v1

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MDPI and ACS Style

Acho, L.; Buenestado, P.; Pujol, G. Finite-Time Control Design for the Discrete-Time Chaotic Logistic Equation. Preprints 2024, 2024070459. https://doi.org/10.20944/preprints202407.0459.v1

APA Style

Acho, L., Buenestado, P., & Pujol, G. (2024). Finite-Time Control Design for the Discrete-Time Chaotic Logistic Equation. Preprints. https://doi.org/10.20944/preprints202407.0459.v1

Chicago/Turabian Style

Acho, L., Pablo Buenestado and Gisela Pujol. 2024 "Finite-Time Control Design for the Discrete-Time Chaotic Logistic Equation" Preprints. https://doi.org/10.20944/preprints202407.0459.v1

Abstract

Finite-time control theory has been widely used as a mathematical tool to design robust controllers. By manipulating the finite-time convergence proof of this theory, we developed a new control design appropriately tuned for the finite-time control of the chaotic logistics system. In our experimental setup, the logistic equation is programmed into a PIC microcontroller, and a part of the controller was conceived using analog electronics. Because the system to be controlled is in the discrete-time domain, and the finite-time stability proof is stated in the continuous-time representation, our finite-time control approach is a good example for designing control algorithms in both time domain schemes. Hence, our experimental results support our main contribution. Pulse Width Modulation (PWM) is the signal format used to translate digital signals into continuous-time fields.

Keywords

Finite-time control; Chaos control; Logistic equation; PIC-Microcontroller; Experimentation

Subject

Computer Science and Mathematics, Applied Mathematics

Copyright: This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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