A Fully Probabilistic Design for Stochastic Systems with Input Delay


This paper is concerned with the regulation problem of discrete-time stochastic systems involving input delays which is relevant to networked control systems. The problem is formulated in a fully probabilistic framework, and the control solution is obtained by minimising the Kullback–Leibler Divergence (KLD) between the actual and desired joint probability density functions of the system dynamics. A closed-form solution for the randomised controller is obtained for stochastic systems that can be described by arbitrary probability density functions. Furthermore, the analytic solution for a class of linear Gaussian stochastic systems is obtained. For this class of systems, the optimal randomised controller is shown to be a state feedback controller which is modified by an extra linear term that is related to the lagged and future control inputs. The developed method is demonstrated on a simulation example, and the results are compared with the standard fully probabilistic design control method.

Publication DOI: https://doi.org/10.1080/00207179.2020.1742386
Divisions: College of Engineering & Physical Sciences > School of Informatics and Digital Engineering > Mathematics
College of Engineering & Physical Sciences > Systems analytics research institute (SARI)
College of Engineering & Physical Sciences
Additional Information: This is an Accepted Manuscript of an article published by Taylor & Francis Group in International Journal of Control on 19 Mar 2020, available online at: http://www.tandfonline.com/10.1080/00207179.2020.1742386
Uncontrolled Keywords: Kullback–Leibler divergence,Stochastic systems,fully probabilistic design,input delay,Control and Systems Engineering,Computer Science Applications
Publication ISSN: 1366-5820
Full Text Link:
Related URLs: https://www.tan ... rnalCode=tcon20 (Publisher URL)
http://www.scop ... tnerID=8YFLogxK (Scopus URL)
PURE Output Type: Article
Published Date: 2020-03-19
Published Online Date: 2020-03-19
Accepted Date: 2020-03-08
Authors: Herzallah, Randa (ORCID Profile 0000-0001-9128-6814)



Version: Accepted Version

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