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

Abstract

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 present.

Publication DOI: https://doi.org/10.1109/TAC.2020.3032091
Divisions: College of Engineering & Physical Sciences > School of Informatics and Digital Engineering > Mathematics
Additional Information: © 2020 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other uses, in any current or future media, including reprinting/republishing this material for advertising or promotional purposes, creating new collective works, for resale or redistribution to servers or lists, or reuse of any copyrighted component of this work in other works. Funding: This work was supported by the Leverhulme Trust, grant number RPG-2017-337.
Publication ISSN: 0018-9286
Full Text Link:
Related URLs: https://ieeexpl ... cument/9234743/ (Publisher URL)
PURE Output Type: Article
Published Date: 2021-09
Published Online Date: 2020-10-21
Accepted Date: 2020-10-01
Authors: Herzallah, Randa (ORCID Profile 0000-0001-9128-6814)

Download

[img]

Version: Accepted Version

| Preview

Export / Share Citation


Statistics

Additional statistics for this record