Fully probabilistic control for stochastic nonlinear control systems with input dependent noise

Randa Herzallah*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

Abstract

Robust controllers for nonlinear stochastic systems with functional uncertainties can be consistently designed using probabilistic control methods. In this paper a generalised probabilistic controller design for the minimisation of the Kullback-Leibler divergence between the actual joint probability density function (pdf) of the closed loop control system, and an ideal joint pdf is presented emphasising how the uncertainty can be systematically incorporated in the absence of reliable systems models. To achieve this objective all probabilistic models of the system are estimated from process data using mixture density networks (MDNs) where all the parameters of the estimated pdfs are taken to be state and control input dependent. Based on this dependency of the density parameters on the input values, explicit formulations to the construction of optimal generalised probabilistic controllers are obtained through the techniques of dynamic programming and adaptive critic methods. Using the proposed generalised probabilistic controller, the conditional joint pdfs can be made to follow the ideal ones. A simulation example is used to demonstrate the implementation of the algorithm and encouraging results are obtained.

Original languageEnglish
Pages (from-to)199-207
Number of pages9
JournalNeural Networks
Volume63
Early online date17 Dec 2014
DOIs
Publication statusPublished - Mar 2015

Bibliographical note

NOTICE: this is the author’s version of a work that was accepted for publication in Neural networks. Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be reflected in this document. Changes may have been made to this work since it was submitted for publication. A definitive version was subsequently published in Herzallah, R, 'Fully probabilistic control for stochastic nonlinear control systems with input dependent noise' Neural networks, vol. 63 (2015) http://dx.doi.org/10.1016/j.neunet.2014.12.004

Keywords

  • adaptive critic
  • dual heuristic programming
  • fully probabilistic design
  • functional uncertainty
  • mixture of gaussians
  • nonlinear stochastic systems

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