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...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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MDPI AG
2023-01-01
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| Series: | Entropy |
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| Online Access: | https://www.mdpi.com/1099-4300/25/2/186 |
| _version_ | 1797621154268053504 |
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| author | Yi Yang Yong Zhang Yuyang Zhou |
| author_facet | Yi Yang Yong Zhang Yuyang Zhou |
| author_sort | Yi Yang |
| collection | DOAJ |
| 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. |
| first_indexed | 2024-03-11T08:51:39Z |
| format | Article |
| id | doaj.art-3feffcb7da274cebac17838b3e9d5672 |
| institution | Directory Open Access Journal |
| issn | 1099-4300 |
| language | English |
| last_indexed | 2024-03-11T08:51:39Z |
| publishDate | 2023-01-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Entropy |
| spelling | doaj.art-3feffcb7da274cebac17838b3e9d56722023-11-16T20:21:59ZengMDPI AGEntropy1099-43002023-01-0125218610.3390/e25020186Tracking Control for Output Probability Density Function of Stochastic Systems Using FPD MethodYi Yang0Yong Zhang1Yuyang Zhou2School of Information Engineering, Inner Mongolia University of Science and Technology, Baotou 014010, ChinaSchool of Information Engineering, Inner Mongolia University of Science and Technology, Baotou 014010, ChinaSchool of Computing Engineering and Built Environment, Edinburgh Napier University, Edinburgh EH10 5DT, UKOutput 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.https://www.mdpi.com/1099-4300/25/2/186tracking controlprobability density functionfull probability designB-spline model |
| spellingShingle | Yi Yang Yong Zhang Yuyang Zhou Tracking Control for Output Probability Density Function of Stochastic Systems Using FPD Method Entropy tracking control probability density function full probability design B-spline model |
| 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 | tracking control probability density function full probability design B-spline model |
| url | https://www.mdpi.com/1099-4300/25/2/186 |
| work_keys_str_mv | AT yiyang trackingcontrolforoutputprobabilitydensityfunctionofstochasticsystemsusingfpdmethod AT yongzhang trackingcontrolforoutputprobabilitydensityfunctionofstochasticsystemsusingfpdmethod AT yuyangzhou trackingcontrolforoutputprobabilitydensityfunctionofstochasticsystemsusingfpdmethod |