Nonlinear Dynamics and Control Theory

A special issue of Mathematics (ISSN 2227-7390). This special issue belongs to the section "C2: Dynamical Systems".

Deadline for manuscript submissions: 30 June 2026 | Viewed by 659

Special Issue Editor


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Guest Editor
Instituto Politécnico Nacional (IPN), Unidad Profesional Interdisciplinaria en Ingeniería y Tecnologías Avanzadas (UPIITA), Mexico City, Mexico
Interests: chaos synchronization; monitoring and control of nonlinear dynamical systems; nonlinear observers; fault diagnosis; control of fractional-order systems

Special Issue Information

Dear Colleagues,

Generally, nonlinear systems display complex dynamic behavior such as steady state multiplicity, singularities, instabilities, bifurcations, and complex oscillations. In fact, scientific interest in the study, modeling, and analysis of nonlinear systems with complex behaviors has attracted a lot of attention, and the applications have been growing considerably. There are several conditions that may affect the nonlinear dynamics, for instance, disturbances, singular input perturbations, initial conditions, and time delays. Nowadays, the theoretical results of systems with nonlinear complex dynamic behaviors have led to important technological applications. In particular, the analysis techniques of nonlinear dynamics, such as chaotic systems, have had important advances in process engineering, image cryptography, synchronization, stabilization, chaos suppression, secure data transmission, life science, information processing, etc.

Control theory has been seeking advanced techniques to achieve high performance in the closed-loop operation of systems, networks, processes, and so on. In fact, there are a wide variety of control structures that have been designed and applied with success such as sliding mode, adaptative, fuzzy logic, observer-based, neural networks, and metaheuristic methods.

Hence, in this Special Issue, we aim to present the developments related to modern trends in nonlinear dynamics and control theory.

Prof. Dr. Juan L. Mata-Machuca
Guest Editor

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Keywords

  • analysis of nonlinear dynamics
  • modeling of nonlinear systems
  • nonlinear observers
  • nonlinear controllers
  • estimation
  • stabilization
  • parameter identification
  • chaotic systems
  • fractional-order systems
  • applications of control theory

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Published Papers (1 paper)

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Research

22 pages, 3231 KB  
Article
A Unified Framework for Identification, Estimation, and Control of an Experimental Duffing–Holmes System
by Antonio Concha-Sánchez, Ulises Mondragón-Cárdenas, Suresh Thenozhi, Juan Luis Mata-Machuca and Suresh Kumar Gadi
Mathematics 2026, 14(6), 1073; https://doi.org/10.3390/math14061073 - 22 Mar 2026
Viewed by 246
Abstract
This paper presents a comprehensive framework for the identification, state estimation, and robust control of a bistable Duffing–Holmes oscillator, validated through an experimental setup. First, to address parametric uncertainty, a Recursive Least Squares Method (RLSM) with a forgetting factor is applied to a [...] Read more.
This paper presents a comprehensive framework for the identification, state estimation, and robust control of a bistable Duffing–Holmes oscillator, validated through an experimental setup. First, to address parametric uncertainty, a Recursive Least Squares Method (RLSM) with a forgetting factor is applied to a filtered model representation, enabling accurate parameter convergence from noisy measurements. Subsequently, a Nonlinear Integral Extended State Observer (NIESO) is designed to reconstruct unmeasured states and estimate total disturbances. A key theoretical contribution is the derivation of explicit gain conditions that guarantee the observer’s stability, overcoming limitations of previous designs. For trajectory tracking, an observer-based backstepping controller is synthesized. Crucially, to bridge the gap between theory and practice, a drift-free integration scheme is implemented to generate feasible position commands for the shake table, preventing actuator saturation. Experimental results confirm the framework’s effectiveness, achieving a 3.7-fold reduction in RMS tracking error compared to open-loop operation, with the tracking error rapidly converging to a small neighborhood within approximately 0.2 s. Furthermore, the closed-loop system demonstrates superior energy efficiency, requiring significantly lower actuator voltage to sustain stable interwell oscillations. Full article
(This article belongs to the Special Issue Nonlinear Dynamics and Control Theory)
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