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Mathematics
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Stochastic Control Systems: Theory and Applications
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Stochastic Control Systems: Theory and Applications

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

Deadline for manuscript submissions: closed (31 December 2023) | Viewed by 8135

Special Issue Editor

Dr. Kagan Eugene

E-Mail Website
Guest Editor
Department of Industrial Engineering and Management, Ariel University, Ariel 4076414, Israel
Interests: cybernetics and robotics; probabilistic algorithms; uncertainty analysis
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues,

We cordially invite you to present your research results in the Special Issue “Stochastic Control Systems: Theory and Applications” of the MDPI’s Mathematics journal. The goal of this Special Issue is to bring together theoretical results and engineering practices with the aim of inspiring new ideas and solutions of existing and rising problems.

In his classical “Introduction to Stochastic Control” (1970) Karl J. Åstrëm formulated three main directions in the theory of stochastic control:

  • Analysis: given the controlled and control systems, find statistical properties of the system variables;
  • Parametric optimization: given the controlled and control systems, adjust parameters of the systems in order to meet definite optimality criteria;
  • Stochastic optimal control: given the controlled system, find the control system that provides an optimality with respect to definite criteria.

And, in general, the studies in the field are concentrated around these objectives.

The Special Issue welcomes the high-quality research papers and surveys in the indicated directions of stochastic control theory with no limits in topics from theoretical findings up to original applications. Numerical illustrations and meaningful discussions of the presented results will be highly appreciated.

Dr. Kagan Eugene
Guest Editor

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 dynamical system
  • stochastic distributed system
  • search and foraging process
  • pursuit and evasion game
  • stochastic flow control

Published Papers (4 papers)

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Research

23 pages, 8373 KiB  
Article
Model Predictive Control of Parabolic PDE Systems under Chance Constraints
by Ruslan Voropai, Abebe Geletu and Pu Li
Mathematics 2023, 11(6), 1372; https://doi.org/10.3390/math11061372 - 12 Mar 2023
Viewed by 1688
Abstract
Model predictive control (MPC) heavily relies on the accuracy of the system model. Nevertheless, process models naturally contain random parameters. To derive a reliable solution, it is necessary to design a stochastic MPC. This work studies the chance constrained MPC of systems described [...] Read more.
Model predictive control (MPC) heavily relies on the accuracy of the system model. Nevertheless, process models naturally contain random parameters. To derive a reliable solution, it is necessary to design a stochastic MPC. This work studies the chance constrained MPC of systems described by parabolic partial differential equations (PDEs) with random parameters. Inequality constraints on time- and space-dependent state variables are defined in terms of chance constraints. Using a discretization scheme, the resulting high-dimensional chance constrained optimization problem is solved by our recently developed inner–outer approximation which renders the problem computationally amenable. The proposed MPC scheme automatically generates probability tubes significantly simplifying the derivation of feasible solutions. We demonstrate the viability and versatility of the approach through a case study of tumor hyperthermia cancer treatment control, where the randomness arises from the thermal conductivity coefficient characterizing heat flux in human tissue. Full article
(This article belongs to the Special Issue Stochastic Control Systems: Theory and Applications)
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23 pages, 868 KiB  
Article
Optimality of a Network Monitoring Agent and Validation in a Real Probe
by Luis Zabala, Josu Doncel and Armando Ferro
Mathematics 2023, 11(3), 610; https://doi.org/10.3390/math11030610 - 26 Jan 2023
Cited by 2 | Viewed by 940
Abstract
The evolution of commodity hardware makes it possible to use this type of equipment to implement traffic monitoring systems. A preliminary empirical evaluation of a network traffic probe based on Linux indicates that the system performance has significant losses as the network rate [...] Read more.
The evolution of commodity hardware makes it possible to use this type of equipment to implement traffic monitoring systems. A preliminary empirical evaluation of a network traffic probe based on Linux indicates that the system performance has significant losses as the network rate increases. To assess this issue, we consider a model with two tandem queues and a moving server. In this system, we formulate a three-dimensional Markov Decision Process in continuous time. The goal of the proposed model is to determine the position of the server in each time slot so as to optimize the system performance which is measured in terms of throughput. We first formulate an equivalent discrete-time Markov Decision Process and we propose a numerical method to characterize the solution of our problem in a general setting. The solution we obtain in this problem has been tested for a wide range of scenarios and, in all the instances, we observe that the optimality is close to a threshold type policy. We also consider a real probe and we validate the good performance of threshold policies in real applications. Full article
(This article belongs to the Special Issue Stochastic Control Systems: Theory and Applications)
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25 pages, 396 KiB  
Article
Closed-Loop Solvability of Stochastic Linear-Quadratic Optimal Control Problems with Poisson Jumps
by Zixuan Li and Jingtao Shi
Mathematics 2022, 10(21), 4062; https://doi.org/10.3390/math10214062 - 01 Nov 2022
Viewed by 1004
Abstract
The stochastic linear–quadratic optimal control problem with Poisson jumps is addressed in this paper. The coefficients in the state equation and the weighting matrices in the cost functional are all deterministic but are allowed to be indefinite. The notion of closed-loop strategies is [...] Read more.
The stochastic linear–quadratic optimal control problem with Poisson jumps is addressed in this paper. The coefficients in the state equation and the weighting matrices in the cost functional are all deterministic but are allowed to be indefinite. The notion of closed-loop strategies is introduced, and the sufficient and necessary conditions for the closed-loop solvability are given. The optimal closed-loop strategy is characterized by a Riccati integral–differential equation and a backward stochastic differential equation with Poisson jumps. A simple example is given to demonstrate the effectiveness of the main result. Full article
(This article belongs to the Special Issue Stochastic Control Systems: Theory and Applications)
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15 pages, 5123 KiB  
Article
A Queueing Model for Traffic Flow Control in the Road Intersection
by Yona Elbaum, Alexander Novoselsky and Evgeny Kagan
Mathematics 2022, 10(21), 3997; https://doi.org/10.3390/math10213997 - 27 Oct 2022
Cited by 3 | Viewed by 4013
Abstract
In this paper, we consider a simple road intersection with traffic light control and suggest a queueing model for the traffic flow in the intersection. The suggested model implements the well-known queue with state-dependent departure rates. Using this model, we define optimal state-dependent [...] Read more.
In this paper, we consider a simple road intersection with traffic light control and suggest a queueing model for the traffic flow in the intersection. The suggested model implements the well-known queue with state-dependent departure rates. Using this model, we define optimal state-dependent scheduling of the traffic lights in the intersection and consider its properties. Activity of the model is illustrated by numerical simulations. It is demonstrated that in practical conditions the suggested scheduling of the traffic lights allows the prevention of traffic jams in the intersection and resolves vehicles queues with reasonable waiting times in the crossing lanes. Full article
(This article belongs to the Special Issue Stochastic Control Systems: Theory and Applications)
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