Mathematical Modelling of Nonlinear Dynamical Systems, 2nd Edition

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

Deadline for manuscript submissions: 31 January 2027 | Viewed by 189

Special Issue Editors


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Guest Editor
Centro Universitario de Los Lagos (CULAGOS), Universidad de Guadalajara, Guadalajara 44100, Mexico
Interests: nonlinear dynamical systems; numerical modeling; laser dynamics; chaos theory; deterministic Brownian motion; fractional calculus
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Guest Editor
Facultad de Ingeniería, Universidad Panamericana, Villa Bonaterra 20296, Mexico
Interests: nonlinear dynamics; mathematical modelling; numerical analysis; stability analysis; stability; dynamics; modeling and simulation; nonlinear analysis; systems dynamics; nonlinear systems

Special Issue Information

Dear Colleagues,

We are pleased to announce a call for submissions to the second volume of our Special Issue titled "Mathematical Modelling of Nonlinear Dynamical Systems, 2nd Edition." We invite our colleagues, friends and researchers in the field of nonlinear dynamical systems to contribute their latest findings, comprehensive reviews and original perspectives. This volume aims to continue showcasing cutting-edge research that addresses the inherent complexities and challenges in mathematically modeling nonlinear dynamical systems across diverse scientific and engineering domains. In particular, we continue to welcome contributions on fractional calculus, which has proven to be an invaluable framework for capturing complex behaviors characterized by nonlocality and long-memory effects, along with its extensive applications in fields such as engineering, physics, biology, economics and beyond. This second volume seeks to further expand the platform for disseminating innovative research that deepen our understanding of the behavior, control and optimization of nonlinear dynamical systems.

Prof. Dr. Guillermo Huerta-Cuellar
Prof. Dr. Héctor Eduardo Gilardi-Velázquez
Guest Editors

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Keywords

  • theoretical developments
  • computational methods
  • control and optimization
  • interdisciplinary research
  • artificial intelligence
  • machine learning
  • big data
  • fractional-order dynamical systems
  • dynamical systems
  • bifurcation analysis
  • chaotic behavior
  • fractional order systems
  • iterative dynamics
  • ordinary differential equations
  • partial differential equations
  • numerical methods

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Published Papers (1 paper)

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Research

24 pages, 1386 KB  
Article
Approximate MSEV State-Space Based Optimal Control of Nonlinear and Nonstationary Dynamic Systems
by Nemanja Deura, Zoran Banjac, Miloš Pavlović, Boško Božilović, Željko Đurović and Branko Kovačević
Mathematics 2026, 14(11), 1802; https://doi.org/10.3390/math14111802 - 22 May 2026
Abstract
A new class of modified minimum state error variance (MSEV) state-space based optimal linear quadratic Gaussian (LQG) regulators for closed-loop structures with estimated feedback has been proposed in this article. The negative feedback path is designed as the cascade of the digital LQG [...] Read more.
A new class of modified minimum state error variance (MSEV) state-space based optimal linear quadratic Gaussian (LQG) regulators for closed-loop structures with estimated feedback has been proposed in this article. The negative feedback path is designed as the cascade of the digital LQG regulator and discrete Kalman state observer. The proposed design enables tracking of a time-varying reference input using the predictive control approach. Moreover, the proposed tracking method utilizes a multivariable continuous-time Cauchy state-space model of nonlinear, nonstationary dynamic systems. The resulting control strategy is approximately optimal, as the optimality of the LQG design holds locally for each linearized model around the respective operating point and does not extend to the global nonlinear system. In this sense, starting from the prespecified nominal state trajectory to be tracked, a numerical optimization procedure minimizing the squared tracking error at each step by using the Nelder–Mead direct search simplex algorithm under the required constraints on the input signal has been developed. The LQG regulator and Kalman state observer are designed by utilizing the linear discrete-time state variable models that properly approximate the nonlinear system dynamics across the nominal state trajectory. The performance of the proposed design is validated by simulating a six-degree-of-freedom nonlinear aircraft model across typical flight regimes. Full article
(This article belongs to the Special Issue Mathematical Modelling of Nonlinear Dynamical Systems, 2nd Edition)
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