A Fully Probabilistic Design for Tracking Control for Stochastic Systems with Input Delay

Randa Herzallah

Research output: Contribution to journalArticlepeer-review


This paper studies model reference adaptive control
(MRAC) for a class of stochastic discrete time control systems
with time delays in the control input. In particular, a unified
fully probabilistic control framework is established to develop the
solution to the MRAC, where the controller is the minimiser of
the Kullback-Leibler Divergence (KLD) between the actual and
desired joint probability density functions of the tracking error
and the controller. The developed framework is quite general,
where all the components within this framework, including the
controller and system tracking error, are modelled using probabilistic models. The general solution for arbitrary probabilistic
models of the framework components is first obtained and then
demonstrated on a class of linear Gaussian systems with time
delay in the main control input, thus obtaining the desired results.
The contribution of this paper is twofold. First, we develop a
fully probabilistic design framework for MRAC, referred to as
MRFPD, for stochastic dynamical systems. Second, we establish a
systematic pedagogic procedure that is based on deriving explicit
forms for the required predictive distributions for obtaining the
causal form of the randomised controller when input delays are
Original languageEnglish
Pages (from-to)4342 - 4348
JournalIEEE Transactions on Automatic Control
Issue number9
Early online date21 Oct 2020
Publication statusPublished - Sep 2021

Bibliographical note

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Funding: This work was supported by the Leverhulme Trust, grant
number RPG-2017-337.


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