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Tracking Control for Output Probability Density Function of Stochastic Systems Using FPD Method

Output probability density function (PDF) tracking control of stochastic systems has always been a challenging problem in both theoretical development and engineering practice. Focused on this challenge, this work proposes a novel stochastic control framework so that the output PDF can track a given...

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Detalles Bibliográficos
Autores principales: Yang, Yi, Zhang, Yong, Zhou, Yuyang
Formato: Online Artículo Texto
Lenguaje:English
Publicado: MDPI 2023
Materias:
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC9955558/
https://www.ncbi.nlm.nih.gov/pubmed/36832552
http://dx.doi.org/10.3390/e25020186
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author Yang, Yi
Zhang, Yong
Zhou, Yuyang
author_facet Yang, Yi
Zhang, Yong
Zhou, Yuyang
author_sort Yang, Yi
collection PubMed
description Output probability density function (PDF) tracking control of stochastic systems has always been a challenging problem in both theoretical development and engineering practice. Focused on this challenge, this work proposes a novel stochastic control framework so that the output PDF can track a given time-varying PDF. Firstly, the output PDF is characterised by the weight dynamics following the B-spline model approximation. As a result, the PDF tracking problem is transferred to a state tracking problem for weight dynamics. In addition, the model error of the weight dynamics is described by the multiplicative noises to more effectively establish its stochastic dynamics. Moreover, to better reflect the practical applications in the real world, the given tracking target is set to be time-varying rather than static. Thus, an extended fully probabilistic design (FPD) is developed based on the conventional FPD to handle multiplicative noises and to track the time-varying references in a superior way. Finally, the proposed control framework is verified by a numerical example, and a comparison simulation with the linear–quadratic regulator (LQR) method is also included to illustrate the superiority of our proposed framework.
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spelling pubmed-99555582023-02-25 Tracking Control for Output Probability Density Function of Stochastic Systems Using FPD Method Yang, Yi Zhang, Yong Zhou, Yuyang Entropy (Basel) Article Output probability density function (PDF) tracking control of stochastic systems has always been a challenging problem in both theoretical development and engineering practice. Focused on this challenge, this work proposes a novel stochastic control framework so that the output PDF can track a given time-varying PDF. Firstly, the output PDF is characterised by the weight dynamics following the B-spline model approximation. As a result, the PDF tracking problem is transferred to a state tracking problem for weight dynamics. In addition, the model error of the weight dynamics is described by the multiplicative noises to more effectively establish its stochastic dynamics. Moreover, to better reflect the practical applications in the real world, the given tracking target is set to be time-varying rather than static. Thus, an extended fully probabilistic design (FPD) is developed based on the conventional FPD to handle multiplicative noises and to track the time-varying references in a superior way. Finally, the proposed control framework is verified by a numerical example, and a comparison simulation with the linear–quadratic regulator (LQR) method is also included to illustrate the superiority of our proposed framework. MDPI 2023-01-17 /pmc/articles/PMC9955558/ /pubmed/36832552 http://dx.doi.org/10.3390/e25020186 Text en © 2023 by the authors. https://creativecommons.org/licenses/by/4.0/Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https://creativecommons.org/licenses/by/4.0/).
spellingShingle Article
Yang, Yi
Zhang, Yong
Zhou, Yuyang
Tracking Control for Output Probability Density Function of Stochastic Systems Using FPD Method
title Tracking Control for Output Probability Density Function of Stochastic Systems Using FPD Method
title_full Tracking Control for Output Probability Density Function of Stochastic Systems Using FPD Method
title_fullStr Tracking Control for Output Probability Density Function of Stochastic Systems Using FPD Method
title_full_unstemmed Tracking Control for Output Probability Density Function of Stochastic Systems Using FPD Method
title_short Tracking Control for Output Probability Density Function of Stochastic Systems Using FPD Method
title_sort tracking control for output probability density function of stochastic systems using fpd method
topic Article
url https://www.ncbi.nlm.nih.gov/pmc/articles/PMC9955558/
https://www.ncbi.nlm.nih.gov/pubmed/36832552
http://dx.doi.org/10.3390/e25020186
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