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Mathematics
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Nonlinear Dynamical Systems: Modeling, Control and Applications
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Nonlinear Dynamical Systems: Modeling, Control and Applications

A special issue of Mathematics (ISSN 2227-7390). This special issue belongs to the section "E2: Control Theory and Mechanics".

Deadline for manuscript submissions: 30 May 2025 | Viewed by 2920

Special Issue Editors

Dr. Luis N. Coria

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Guest Editor
Instituto Tecnológico de Tijuana, Calz. del Tecnológico S/N, Tomás Aquino, Tijuana 22414, Mexico
Interests: nonlinear analysis; numerical simulation; mathematical modeling; dynamics; mathematical analysis; modeling and simulation; control theory; applied mathematics; engineering; applied and computational mathematics; numerical analysis
Prof. Dr. Paul A. Valle-Trujillo

E-Mail Website
Guest Editor
Postgraduate Program in Engineering Sciences, BioMath Research Group, Tecnológico Nacional de México/IT Tijuana, Blvd. Alberto Limón Padilla s/n, Tijuana 22454, Mexico
Interests: biomathematics; biostatistics; ordinary differential equations; localization of compact; invariant sets; cancer modeling and analysis; local and global stability; in silico; computational biology

Special Issue Information

Dear Colleagues,

This Special Issue aims to explore the multiple applications of dynamical systems in engineering sciences [biomedical, chemistry, control, electric, electronic, mechanical, etc.]. Mathematical modeling, analysis, control, and simulation are critical steps to fully understand both the short- and long-term behavior of a dynamical system; this allows us to evaluate its performance under different scenarios [initial conditions, parameter values, and disturbances] and their suitability to solve real-life problems.

We are pleased to invite you to contribute to an exciting and fascinating topic, where nonlinear control theory can be the main tool for solving the most challenging engineering problems, from cancer to robotics, from energy efficiency to underwater vehicles, from biochemical reactors to disease-spreading modeling, and more. Please reach us if you have questions about your submission.

Dr. Luis N. Coria
Prof. Dr. Paul A. Valle-Trujillo
Guest Editors

Manuscript Submission Information

Manuscripts should be submitted online at www.mdpi.com by registering and logging in to this website. Once you are registered, click here to go to the submission form. Manuscripts can be submitted until the deadline. All submissions that pass pre-check are peer-reviewed. Accepted papers will be published continuously in the journal (as soon as accepted) and will be listed together on the special issue website. Research articles, review articles as well as short communications are invited. For planned papers, a title and short abstract (about 100 words) can be sent to the Editorial Office for announcement on this website.

Submitted manuscripts should not have been published previously, nor be under consideration for publication elsewhere (except conference proceedings papers). All manuscripts are thoroughly refereed through a single-blind peer-review process. A guide for authors and other relevant information for submission of manuscripts is available on the Instructions for Authors page. Mathematics is an international peer-reviewed open access semimonthly journal published by MDPI.

Please visit the Instructions for Authors page before submitting a manuscript. The Article Processing Charge (APC) for publication in this open access journal is 2600 CHF (Swiss Francs). Submitted papers should be well formatted and use good English. Authors may use MDPI's English editing service prior to publication or during author revisions.

Keywords

  • applied mathematics
  • biological, biochemical, and physiological systems
  • biomathematics and biostatistics
  • chaos
  • compact invariant sets
  • computational methods in control
  • control theory
  • ordinary differential equations
  • electronic and mechanical systems
  • in silico experimentation
  • mathematical and computational modeling
  • nonlinear control theory
  • nonlinear dynamical systems
  • nonlinear observers
  • stability and asymptotic stability theory
  • synchronization

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Further information on MDPI's Special Issue policies can be found here.

Published Papers (3 papers)

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Research

20 pages, 13476 KiB  
Article
Time-Reversible Synchronization of Analog and Digital Chaotic Systems
by Artur Karimov, Vyacheslav Rybin, Ivan Babkin, Timur Karimov, Veronika Ponomareva and Denis Butusov
Mathematics 2025, 13(9), 1437; https://doi.org/10.3390/math13091437 - 27 Apr 2025
Viewed by 265
Abstract
The synchronization of chaotic systems is a fundamental phenomenon in nonlinear dynamics. Most known synchronization techniques suggest that the trajectories of coupled systems converge at an exponential rate. However, this requires transferring a substantial data array to achieve complete synchronization between the master [...] Read more.
The synchronization of chaotic systems is a fundamental phenomenon in nonlinear dynamics. Most known synchronization techniques suggest that the trajectories of coupled systems converge at an exponential rate. However, this requires transferring a substantial data array to achieve complete synchronization between the master and slave oscillators. A recently developed approach, called time-reversible synchronization, has been shown to accelerate the convergence of trajectories. This approach is based on the special properties of time-symmetric integration. This technique allows for achieving the complete synchronization of discrete chaotic systems at a superexponential rate. However, the validity of time-reversible synchronization between discrete and continuous systems has remained unproven. In the current study, we expand the applicability of fast time-reversible synchronization to a case of digital and analog chaotic systems. A circuit implementation of the Sprott Case B was taken as an analog chaotic oscillator. Given that real physical systems possess more complicated dynamics than simplified models, analog system reidentification was performed to achieve a reasonable relevance between a discrete model and the circuit. The result of this study provides strong experimental evidence of fast time-reversible synchronization between analog and digital chaotic systems. This finding opens broad possibilities in reconstructing the phase dynamics of partially observed chaotic systems. Utilizing minimal datasets in such possible applications as chaotic communication, sensing, and system identification is a notable development of this research. Full article
(This article belongs to the Special Issue Nonlinear Dynamical Systems: Modeling, Control and Applications)
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25 pages, 1435 KiB  
Article
A New Motion Tracking Controller with Feedforward Compensation for Robot Manipulators Based on Sectorial Fuzzy Control and Adaptive Neural Networks
by Andres Pizarro-Lerma, Victor Santibañez, Ramon Garcia-Hernandez, Jorge Villalobos-Chin and Javier Moreno-Valenzuela
Mathematics 2025, 13(6), 977; https://doi.org/10.3390/math13060977 - 16 Mar 2025
Viewed by 398
Abstract
A novel trajectory tracking control approach for robot manipulators that uses adaptive neural network feedforward compensation plus a sectorial fuzzy controller is presented. We conduct simulation and real-time experiments comparing it with two previously published control schemes: a Proportional–Derivative (PD) plus feedforward compensation [...] Read more.
A novel trajectory tracking control approach for robot manipulators that uses adaptive neural network feedforward compensation plus a sectorial fuzzy controller is presented. We conduct simulation and real-time experiments comparing it with two previously published control schemes: a Proportional–Derivative (PD) plus feedforward compensation controller model, and a sectorial fuzzy control plus feedforward compensation model. The proposed controller shows a faster transient response and better steady-state angular error performance than its counterparts, and it maintains its tolerance to parameter deviation, a main characteristic of fuzzy controllers; furthermore, it excludes the need for knowledge of the robot manipulator model to achieve excellent results. A formal stability analysis of the proposed controller in a closed loop with the robot manipulator guarantees that position and velocity errors converge to zero and all signals are uniformly bounded. Full article
(This article belongs to the Special Issue Nonlinear Dynamical Systems: Modeling, Control and Applications)
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28 pages, 8589 KiB  
Article
Sensorless Control of Permanent Magnet Synchronous Motor Drives with Rotor Position Offset Estimation via Extended State Observer
by Ramón Ramírez-Villalobos, Luis N. Coria, Paul A. Valle and Christian Aldrete-Maldonado
Mathematics 2025, 13(6), 899; https://doi.org/10.3390/math13060899 - 7 Mar 2025
Cited by 1 | Viewed by 1232
Abstract
The aim of this study is to develop sensorless high-speed tracking control for surface-mounted permanent magnet synchronous motors by taking the rotor position offset error and time-varying load torque into consideration. This proposal combines an extended state observer with an adaptation position algorithm, [...] Read more.
The aim of this study is to develop sensorless high-speed tracking control for surface-mounted permanent magnet synchronous motors by taking the rotor position offset error and time-varying load torque into consideration. This proposal combines an extended state observer with an adaptation position algorithm, employing only the measurement of electrical variables for feedback. First, a rotatory coordinate model of the motor is proposed, wherein the rotor position offset error is considered as a perturbation function within the model. Second, based on the aforementioned model, a rotary coordinate model of the motor is extended in one state to estimate the load torque, as well as the rotor’s position and speed, despite the presence of the rotor position offset error. Through Lyapunov stability analysis, sufficient conditions were established to guarantee that the error estimations were bounded. Finally, to validate the feasibility of the proposed sensorless scheme, experiments were conducted on the Technosoft® development platform, where the alignment routine was disabled and an intentional misalignment between the magnetic north pole and the stator’s south pole was established. Full article
(This article belongs to the Special Issue Nonlinear Dynamical Systems: Modeling, Control and Applications)
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