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Mathematics
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Stochastic System Analysis and Control
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Stochastic System Analysis and Control

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

Deadline for manuscript submissions: 31 August 2025 | Viewed by 4611

Special Issue Editors

Dr. Tianliang Zhang

E-Mail Website
Guest Editor
School of Information and Control Engineering, Qingdao University of Technology, Qingdao 266555, China
Interests: stochastic systems; control
Prof. Dr. Xiangyun Lin

E-Mail Website
Guest Editor
School of Mathematics and Systems Science, Shandong University of Science and Technology, Qingdao 266590, China
Interests: stochastic differential equations; stochastic control; financial engineering; financial statistics
Dr. Xiushan Jiang

E-Mail Website
Guest Editor
Department of Chemical Equipment and Control Engineering, China University of Petroleum (East China), Qingdao 266580, China
Interests: stochastic reinforcement learning theory; stochastic models in industrial processes

Special Issue Information

Dear Colleagues,

We are pleased to invite you to contribute to a Special Issue on "Stochastic System Analysis and Control". This Special Issue aims to highlight the latest advancements and research in the field of stochastic systems, focusing on both theoretical and practical aspects of analysis and control.

Stochastic systems are ubiquitous in various fields, including that of engineering, economics, biology, and more. The analysis and control of these systems are crucial for improving performance, reliability, and efficiency in complex and uncertain environments. This Special Issue will gather high-quality research papers that address significant challenges and propose innovative solutions in the analysis and control of stochastic systems.

The goal of this Special Issue is to provide a platform for researchers to share their latest findings and insights on stochastic systems. We seek to publish papers that contribute to the theoretical understanding, practical methodologies, and applications of stochastic systems analysis and control.

This Special Issue aligns with the scope of our journal, aiming to bridge the gap between theoretical research and practical implementations. In this Special Issue, we welcome original research articles and comprehensive review papers. Potential topics include, but are not limited to, the following:

  • Stochastic modeling and simulation;
  • Stochastic processes and noise analysis;
  • Control strategies for stochastic systems;
  • Applications in engineering and technology;
  • Optimization techniques in stochastic environments;
  • Statistical methods for system analysis;
  • Stochastic reinforcement learning theory;
  • Analysis of stochastic partial differential equations;
  • Case studies and practical implementations.

Dr. Tianliang Zhang
Prof. Dr. Xiangyun Lin
Dr. Xiushan Jiang
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

  • stochastic modeling
  • noise analysis
  • stochastic processes
  • control strategies
  • optimization
  • system analysis
  • engineering applications
  • statistical methods
  • stochastic reinforcement learning
  • stochastic partial differential equations
  • practical implementations

Benefits of Publishing in a Special Issue

  • Ease of navigation: Grouping papers by topic helps scholars navigate broad scope journals more efficiently.
  • Greater discoverability: Special Issues support the reach and impact of scientific research. Articles in Special Issues are more discoverable and cited more frequently.
  • Expansion of research network: Special Issues facilitate connections among authors, fostering scientific collaborations.
  • External promotion: Articles in Special Issues are often promoted through the journal's social media, increasing their visibility.
  • e-Book format: Special Issues with more than 10 articles can be published as dedicated e-books, ensuring wide and rapid dissemination.

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

Published Papers (5 papers)

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Research

20 pages, 908 KiB  
Article
Output Feedback Optimal Control for Discrete-Time Singular Systems Driven by Stochastic Disturbances and Markov Chains
by Jing Xie, Bowen Zhang, Tianliang Zhang and Xiangtong Kong
Mathematics 2025, 13(4), 634; https://doi.org/10.3390/math13040634 - 14 Feb 2025
Viewed by 442
Abstract
This paper delves into the exploration of the indefinite linear quadratic optimal control (LQOC) problem for discrete-time stochastic singular systems driven by discrete-time Markov chains. Initially, the conversion of the indefinite LQOC problem mentioned above for stochastic singular systems into an equivalent problem [...] Read more.
This paper delves into the exploration of the indefinite linear quadratic optimal control (LQOC) problem for discrete-time stochastic singular systems driven by discrete-time Markov chains. Initially, the conversion of the indefinite LQOC problem mentioned above for stochastic singular systems into an equivalent problem of normal stochastic systems is executed through a sequence of transformations. Following this, the paper furnishes sufficient and necessary conditions for resolving the transformed LQOC problem with indefinite matrix parameters, alongside optimal control strategies ensuring system regularity and causality, thereby establishing the solvability of the optimal controller. Additionally, conditions are derived to verify the definiteness of the transformed LQOC problem and the uniqueness of solutions for the generalized Markov jumping algebraic Riccati equation (GMJARE). The study attains optimal controls and nonnegative cost values, guaranteeing system admissibility. The results of the finite horizon are extended to the infinite horizon. Furthermore, it introduces the design of an output feedback controller using the LMI method. Finally, a demonstrative example demonstrates the validity of the main findings. Full article
(This article belongs to the Special Issue Stochastic System Analysis and Control)
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18 pages, 419 KiB  
Article
Sliding Mode Control of Uncertain Switched Systems via Length-Limited Coding Dynamic Quantization
by Qinqi Xu and Haijuan Zhao
Mathematics 2024, 12(23), 3749; https://doi.org/10.3390/math12233749 - 28 Nov 2024
Cited by 1 | Viewed by 743
Abstract
This paper designs an online adjustment strategy for dynamic quantizer parameters and investigates the sliding mode control (SMC) problem for uncertain switched systems under a limited network communication bandwidth. Due to the limitation of the coding length in practical transmission, coding errors can [...] Read more.
This paper designs an online adjustment strategy for dynamic quantizer parameters and investigates the sliding mode control (SMC) problem for uncertain switched systems under a limited network communication bandwidth. Due to the limitation of the coding length in practical transmission, coding errors can significantly impact the system’s ideal performance. To address these issues, a dynamic quantizer is introduced to efficiently encode the system state while minimizing quantization error under the constraint of the finite code length. Additionally, a coding and decoding scheme based on dynamic quantization and a suitable sliding mode controller are designed to obtain a closed-loop switched system. Using Lyapunov functions and the average dwell time method, sufficient conditions are derived to guarantee the reachability of the sliding surface and the exponential ultimate bound (EUB) in the mean square for the closed-loop switched system, even in the presence of coding errors and data loss. The theoretical results are validated through numerical simulations, which demonstrate the effectiveness of the proposed approach. Full article
(This article belongs to the Special Issue Stochastic System Analysis and Control)
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10 pages, 277 KiB  
Article
H∞ Filtering of Mean Field Stochastic Differential Systems
by Siqi Lv and Ting Hou
Mathematics 2024, 12(21), 3329; https://doi.org/10.3390/math12213329 - 23 Oct 2024
Viewed by 664
Abstract
This paper addresses the H∞ filtering problem for mean field stochastic differential systems that involve both state-dependent and disturbance-dependent noise. We assume that the state as well as the measurement output is distracted by an uncertain exogenous disturbance. Firstly, a sufficient condition [...] Read more.
This paper addresses the H∞ filtering problem for mean field stochastic differential systems that involve both state-dependent and disturbance-dependent noise. We assume that the state as well as the measurement output is distracted by an uncertain exogenous disturbance. Firstly, a sufficient condition for the stochastic-bounded real lemma is given. Next, H∞ filtering, which is built upon a stochastic-bounded real lemma, is put forward by two linear matrix inequalities. Furthermore, the validation of the theoretical analysis is demonstrated with two examples. Full article
(This article belongs to the Special Issue Stochastic System Analysis and Control)
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19 pages, 379 KiB  
Article
Analysis and Controller Design for Parameter Varying T-S Fuzzy Systems with Markov Jump
by Na Min and Hongyang Zhang
Mathematics 2024, 12(17), 2721; https://doi.org/10.3390/math12172721 - 31 Aug 2024
Cited by 1 | Viewed by 821
Abstract
In this paper, we investigate a novel T-S fuzzy parameter varying system with Markov jump, in which parameters depend not only on a Markov chain but also on linear parameter varying elements that take values in convex polytopic sets. Stable conditions and the [...] Read more.
In this paper, we investigate a novel T-S fuzzy parameter varying system with Markov jump, in which parameters depend not only on a Markov chain but also on linear parameter varying elements that take values in convex polytopic sets. Stable conditions and the gain-scheduling controller design method for this system are obtained. Applying Lyapunov function depending on the operation mode and full block S-procedure lemma, we obtain stochastic stabilization conditions. We find that this novel system has two distinct advantages. On the one hand, it inherits the advantages of traditional T-S fuzzy systems in handling nonlinear objects under the frame of T-S fuzzy systems; on the other, it obtains the advantages of dealing with time-varying characteristics from the point of linear parameter varying (LPV) systems. Finally, the theory results are illustrated via numerical simulation. Full article
(This article belongs to the Special Issue Stochastic System Analysis and Control)
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26 pages, 773 KiB  
Article
A Momentum-Based Adaptive Primal–Dual Stochastic Gradient Method for Non-Convex Programs with Expectation Constraints
by Rulei Qi, Dan Xue and Yujia Zhai
Mathematics 2024, 12(15), 2393; https://doi.org/10.3390/math12152393 - 31 Jul 2024
Viewed by 1133
Abstract
In this paper, we propose a stochastic primal-dual adaptive method based on an inexact augmented Lagrangian function to solve non-convex programs, referred to as the SPDAM. Different from existing methods, SPDAM incorporates adaptive step size and momentum-based search directions, which improve the convergence [...] Read more.
In this paper, we propose a stochastic primal-dual adaptive method based on an inexact augmented Lagrangian function to solve non-convex programs, referred to as the SPDAM. Different from existing methods, SPDAM incorporates adaptive step size and momentum-based search directions, which improve the convergence rate. At each iteration, an inexact augmented Lagrangian subproblem is solved to update the primal variables. A post-processing step is designed to adjust the primal variables to meet the accuracy requirement, and the adjusted primal variable is used to compute the dual variable. Under appropriate assumptions, we prove that the method converges to the ε-KKT point of the primal problem, and a complexity result of SPDAM less than O(ε−112) is established. This is better than the most famous O(ε−6) result. The numerical experimental results validate that this method outperforms several existing methods with fewer iterations and a lower running time. Full article
(This article belongs to the Special Issue Stochastic System Analysis and Control)
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