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 1059

Special Issue Editors

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
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

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Keywords

  • stochastic control
  • probabilistic control
  • Bayesian inference and control
  • constraint control
  • optimization
  • uncertainty
  • machine learning
  • robotics

Published Papers (2 papers)

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Research

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 340
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
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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 470
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
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