Mathematical Modeling and Control: Theory and Applications

A special issue of Axioms (ISSN 2075-1680). This special issue belongs to the section "Mathematical Analysis".

Deadline for manuscript submissions: 30 April 2026 | Viewed by 1230

Special Issue Editors


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Guest Editor
1. School of Mathematics and Statistic, Nanjing University of Information Science and Technology, Nanjing 210044, China
2. Jiangsu International Joint Laboratory on System Modeling and Data Analysis, Nanjing University of Information Science and Technology, Nanjing 210044, China
Interests: stochastic partial differential equations; stochastic control; mathematical biology; dynamic system
Special Issues, Collections and Topics in MDPI journals

E-Mail Website
Guest Editor
1. School of Mathematics and Statistic, Nanjing University of Information Science and Technology, Nanjing 210044, China
2. Center for Applied Mathematics of Jiangsu Province, Nanjing University of Information Science and Technology, Nanjing 210044, China
3. Jiangsu International Joint Laboratory on System Modeling and Data Analysis, Nanjing University of Information Science and Technology, Nanjing 210044, China
Interests: fractals; image processing; time series; feature extraction; pattern recognition; 3D modeling; topology optimization; machine learning
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues,

There are many current scientific challenges in fields such as mathematical physics and biological sciences, which are emerging and need to be addressed through different technologies and methods. In this process, mathematical modelling, control, etc., play a crucial role.

The Special Issue aims to collect original and quality contributions on the more recent developments of mathematical modeling, control theory, and related topics. The scope includes, but is not limited to, the following:

  1. Stochastic control and optimal control;
  2. Biology models including (stochastic) ordinary and partial differential equations;
  3. Time fractional differential equations and non-local equations;
  4. Numerical method and control theory;
  5. Interdisciplinary applications.

This Special Issue will focus on stochastic control, optimal control, biological mathematics, numerical simulation, and related applications. The main research will be beneficial for the improvement of theory and the resolution of practical problems, and will promote the development of control and other fields.

Prof. Dr. Guangying Lv
Prof. Dr. Jian Wang
Guest Editors

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Keywords

  • stochastic control
  • multi-agent systems
  • optimal control
  • stochastic (partial) differential equations
  • fractional differential equations
  • machine learning

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Published Papers (1 paper)

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Research

20 pages, 358 KB  
Article
Ideal (I2) Convergence in Fuzzy Paranormed Spaces for Practical Stability of Discrete-Time Fuzzy Control Systems Under Lacunary Measurements
by Muhammed Recai Türkmen and Hasan Öğünmez
Axioms 2025, 14(9), 663; https://doi.org/10.3390/axioms14090663 - 29 Aug 2025
Viewed by 378
Abstract
We investigate the stability of linear discrete-time control systems with a fuzzy logic feedback under sporadic sensor data loss. In our framework, each state measurement is a fuzzy number, and occasional “packet dropouts” are modeled by a lacunary subsequence of missing readings. We [...] Read more.
We investigate the stability of linear discrete-time control systems with a fuzzy logic feedback under sporadic sensor data loss. In our framework, each state measurement is a fuzzy number, and occasional “packet dropouts” are modeled by a lacunary subsequence of missing readings. We introduce a novel mathematical approach using lacunary statistical convergence in fuzzy paranormed spaces to analyze such systems. Specifically, we treat the sequence of fuzzy measurements as a double sequence (indexed by time and state component) and consider an admissible ideal of “negligible” index sets that includes the missing–data pattern. Using the concept of ideal fuzzy—paranorm convergence (I-fp convergence), we formalize a lacunary statistical consistency condition on the fuzzy measurements. We prove that if the closed-loop matrix ABK is Schur stable (i.e., ABK<1) in the absence of dropouts, then under the lacunary statistical consistency condition, the controlled system is practically stable despite intermittent measurement losses. In other words, for any desired tolerance, the state eventually remains within that bound (though not necessarily converging to zero). Our result yields an explicit, non-probabilistic (distribution-free) analytical criterion for robustness to sensor dropouts, without requiring packet-loss probabilities or Markov transition parameters. This work merges abstract convergence theory with control application: it extends statistical and ideal convergence to double sequences in fuzzy normed spaces and applies it to ensure stability of a networked fuzzy control system. Full article
(This article belongs to the Special Issue Mathematical Modeling and Control: Theory and Applications)
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