A fully probabilistic control framework for stochastic systems with input and state delay

Abstract

This paper proposes a unified probabilistic control framework for a class of stochastic systems with both control input and state time delays. Both of the stochastic nature and time delays in the system dynamics are considered simultaneously, thus providing a comprehensive and rigorous control methodology. The problem is formulated in a fully probabilistic framework, where the system dynamics and its controller are fully characterised by arbitrary probabilistic models. In this framework, the Kullback–Leibler Divergence between the actual joint probability density function of the system dynamics and controller and a predefined ideal joint probability density function is used to characterise the discrepancy between the two distributions and derive the randomised controller. Time delays in the control input and system state are taken into consideration in the optimisation process for the derivation of the optimal randomised controller. Besides, the analytic control solution of the time delay fully probabilistic control problem for a class of linear Gaussian stochastic systems is derived while the successive approximation approach is implemented to deal with the time-advanced components in the control law that result from the existence of time delays. The effectiveness of the proposed control framework is then illustrated on a numerical example and a real-world example.

Publication DOI: https://doi.org/10.1038/s41598-022-11514-z
Divisions: College of Engineering & Physical Sciences > School of Informatics and Digital Engineering > Mathematics
Additional Information: This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article's Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article's Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/. Funding: This work was supported by the Leverhulme Trust under Grant RPG-2017-337.
Publication ISSN: 2045-2322
Full Text Link:
Related URLs: https://www.nat ... 598-022-11514-z (Publisher URL)
PURE Output Type: Article
Published Date: 2022-05-12
Accepted Date: 2022-04-22
Authors: Herzallah, Randa (ORCID Profile 0000-0001-9128-6814)
Zhou, Yuyang

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