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Axioms
Special Issues
Mathematical Modeling and Control: Theory and Applications
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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: closed (30 April 2026) | Viewed by 2136

Special Issue Editors

Prof. Dr. Guangying Lv

E-Mail Website
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
Prof. Dr. Jian Wang

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

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 250 words) can be sent to the Editorial Office for assessment.

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. Axioms is an international peer-reviewed open access monthly 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 2400 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

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

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

Published Papers (2 papers)

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Research

12 pages, 709 KB  
Article
Novel Design of Compact Data Learning Frameworks for Time-Series Forecasting
by Song-Kyoo Kim
Axioms 2026, 15(5), 357; https://doi.org/10.3390/axioms15050357 - 11 May 2026
Abstract
This paper focuses on optimizing machine learning-based time-series forecasting models by constructing compact data. Compact Data Learning for Time Series (CDL-TS) is a novel framework aimed at minimizing forecasting model errors. By utilizing reduced sampling and robust comparison procedures, CDL-TS addresses the challenges [...] Read more.
This paper focuses on optimizing machine learning-based time-series forecasting models by constructing compact data. Compact Data Learning for Time Series (CDL-TS) is a novel framework aimed at minimizing forecasting model errors. By utilizing reduced sampling and robust comparison procedures, CDL-TS addresses the challenges of forecasting models on extensive real-time data systems. By strategically minimizing data size while maintaining accuracy, CDL-TS presents an innovative framework that facilitates robust predictions and enhances operational efficiency. The combined bivariate performance measure-based optimization effectively balances sampling frequency with the mean square error (MSE) to improve the trade operation performance in stock markets. Through a series of empirical applications, particularly involving the M/M/1 queuing system and various stock trade optimizations with global high-tech companies, the CDL-TS framework has proven its effectiveness by significantly minimizing both forecasting errors and operational costs. This accomplishment highlights the robust capabilities of CDL-TS in enhancing predictive accuracy while facilitating operation cost savings across different domains, including complex systems like queues and real-time financial markets. Full article
(This article belongs to the Special Issue Mathematical Modeling and Control: Theory and Applications)
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
Cited by 1 | Viewed by 931
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 A−BK is Schur stable (i.e., ∥A−BK∥<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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