A Fully Probabilistic Design for Stochastic Systems with Input Delay

Randa Herzallah

Research output: Contribution to journalArticlepeer-review


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.

Original languageEnglish
Pages (from-to)2934-2944
JournalInternational Journal of Control
Issue number11
Early online date19 Mar 2020
Publication statusE-pub ahead of print - 19 Mar 2020

Bibliographical note

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


  • Kullback–Leibler divergence
  • Stochastic systems
  • fully probabilistic design
  • input delay


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