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 - Sept 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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