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Mathematics
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Control, Optimisation, and Applications of Stochastic Uncertain Systems
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Control, Optimisation, and Applications of Stochastic Uncertain Systems

A special issue of Mathematics (ISSN 2227-7390). This special issue belongs to the section "Computational and Applied Mathematics".

Deadline for manuscript submissions: 30 September 2024 | Viewed by 1562

Special Issue Editors

Dr. Randa Herzallah

E-Mail Website
Guest Editor
Zeeman Mathematics Institute, University of Warwick, Coventry CV4 7AL, UK
Interests: stochastic systems; fault-tolerant control; optimal control; neural networks; decentralised control; signal processing; quantum systems; synchronization of complex dynamical systems, bioinformatics data analysis; robotics, dynamic programming; statistical pattern processing; machine learning
Dr. Yuyang Zhou

E-Mail Website
Guest Editor
School of Computing Engineering and Built Environment, Edinburgh Napier University, Edinburgh EH10 5DT, UK
Interests: stochastic system control; robabilistic control; probability density function (PDF) control strategy; minimum entropy control; decentralized control

Special Issue Information

Dear Colleagues,

Uncertainty is a ubiquitous feature of many real-world systems, and accounting for it is essential for designing effective control and optimization strategies. Stochastic control theory has emerged as a powerful tool for addressing the challenges posed by uncertainty, finding applications in diverse fields, such as engineering, economics, finance, and the physical and biological sciences. This Special Issue of Mathematics focuses on the latest advances in the control, optimization, and applications of stochastic uncertain systems.

The goal of this Special Issue is to bring together original research and review articles on pioneering methods for controlling complex, uncertain, and stochastic systems. Topics of interest include the development of new mathematical models and algorithms for stochastic control, performance analysis of stochastic control systems, intelligent control and machine learning, and applications of stochastic control in domains such as robotics, energy systems, and finance. The contributions to this Special Issue highlight the importance of considering uncertainty in the design and implementation of control and optimization strategies, showcasing the versatility and effectiveness of stochastic control approaches.

Dr. Randa Herzallah
Dr. Yuyang Zhou
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 control
  • probabilistic control
  • Bayesian inference and control
  • constraint control
  • optimization
  • uncertainty
  • machine learning
  • robotics

Published Papers (3 papers)

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Research

21 pages, 684 KiB  
Article
Adaptive RBF Neural Network Tracking Control of Stochastic Nonlinear Systems with Actuators and State Constraints
by Jianhua Zhang and Yinguang Li
Mathematics 2024, 12(9), 1378; https://doi.org/10.3390/math12091378 - 30 Apr 2024
Viewed by 312
Abstract
This paper investigates the adaptive neural network (NN) tracking control problem for stochastic nonlinear systems with multiple actuator constraints and full-state constraints. The issue of system full-state constraints is tackled by a generalized barrier Lyapunov function (GBLF), and the output constraints of the [...] Read more.
This paper investigates the adaptive neural network (NN) tracking control problem for stochastic nonlinear systems with multiple actuator constraints and full-state constraints. The issue of system full-state constraints is tackled by a generalized barrier Lyapunov function (GBLF), and the output constraints of the system are considered to be in the form of time-varying functions, which are more in line with the needs of real physical systems. The NN approximation technique is utilized to overcome the influence of the uncertainty term on controller design due to randomness. Based on the backstepping technique, a neural adaptive fixed-time tracking control strategy is designed. Under the designed control strategy, the tracking accuracy of the controlled system can reach the expectation in a fixed time. The multi-actuator constraints are converted into a generalized mathematical model to simplify the controller design process. Using the characteristics of the hyperbolic tangent function, a new function called practical virtual control signal is designed using the virtual control signal as the input. Due to the saturation constraint property of the hyperbolic tangent function, it is theoretically ensured that no state of the system exceeds the constraints through to the new form of the virtual controller. Using the adaptive controller constructed in this paper, the controlled system is semi-global fixed-time stabilized in probability (SGFSP). Finally, the effectiveness of the proposed control strategy is further verified by simulation examples. Full article
(This article belongs to the Special Issue Control, Optimisation, and Applications of Stochastic Uncertain Systems)
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20 pages, 668 KiB  
Article
Event-Triggered Relearning Modeling Method for Stochastic System with Non-Stationary Variable Operating Conditions
by Jiyan Liu, Yong Zhang, Yuyang Zhou and Jing Chen
Mathematics 2024, 12(5), 667; https://doi.org/10.3390/math12050667 - 24 Feb 2024
Viewed by 420
Abstract
This study presents a novel event-triggered relearning framework for neural network modeling, designed to improve prediction precision in dynamic stochastic complex industrial systems under non-stationary and variable conditions. Firstly, a sliding window algorithm combined with entropy is applied to divide the input and [...] Read more.
This study presents a novel event-triggered relearning framework for neural network modeling, designed to improve prediction precision in dynamic stochastic complex industrial systems under non-stationary and variable conditions. Firstly, a sliding window algorithm combined with entropy is applied to divide the input and output datasets across different operational conditions, establishing clear data boundaries. Following this, the prediction errors derived from the neural network under different operational states are harnessed to define a set of event-triggered relearning criteria. Once these conditions are triggered, the relevant dataset is used to recalibrate the model to the specific operational condition and predict the data under this operating condition. When the predicted data fall within the training input range of a pre-trained model, we switch to that model for immediate prediction. Compared with the conventional BP neural network model and random vector functional-link network, the proposed model can produce a better estimation accuracy and reduce computation costs. Finally, the effectiveness of our proposed method is validated through numerical simulation tests using nonlinear Hammerstein models with Gaussian noise, reflecting complex stochastic industrial processes. Full article
(This article belongs to the Special Issue Control, Optimisation, and Applications of Stochastic Uncertain Systems)
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16 pages, 399 KiB  
Article
Closed-Loop Continuous-Time Subspace Identification with Prior Information
by Miao Yu, Wanli Wang and Youyi Wang
Mathematics 2023, 11(24), 4924; https://doi.org/10.3390/math11244924 - 11 Dec 2023
Viewed by 541
Abstract
This paper presents a closed-loop continuous-time subspace identification method using prior information. Based on a rational inner function, a generalized orthonormal basis can be constructed, and the transformed noises have ergodicity features. The continuous-time stochastic system is converted into a discrete-time stochastic system [...] Read more.
This paper presents a closed-loop continuous-time subspace identification method using prior information. Based on a rational inner function, a generalized orthonormal basis can be constructed, and the transformed noises have ergodicity features. The continuous-time stochastic system is converted into a discrete-time stochastic system by using generalized orthogonal basis functions. As is known to all, incorporating prior information into identification strategies can increase the precision of the identified model. To enhance the precision of the identification method, prior information is integrated through the use of constrained least squares, and principal component analysis is adopted to achieve the reliable estimate of the system. Moreover, the identification of open-loop models is the primary intent of the continuous-time system identification approaches. For closed-loop systems, the open-loop subspace identification methods may produce biased results. Principal component analysis, which reliably estimates closed-loop systems, provides a solution to this problem. The restricted least-squares method with an equality constraint is used to incorporate prior information into the impulse response following the principal component analysis. The input–output algebraic equation yielded an optimal multi-step-ahead predictor, and the equality constraints describe the prior information. The effectiveness of the proposed method is provided by numerical simulations. Full article
(This article belongs to the Special Issue Control, Optimisation, and Applications of Stochastic Uncertain Systems)
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