Stochastic distribution tracking control for stochastic non-linear systems via probability density function vectorisation

Yefeng Liu, Qichun Zhang, Hong Yue

Research output: Contribution to journalArticlepeer-review

4 Citations (Scopus)
4 Downloads (Pure)


This paper presents a new control strategy for stochastic distribution shape tracking regarding non-Gaussian stochastic non-linear systems. The objective
can be summarised as adjusting the probability density function (PDF) of the system output to any given desired distribution. In order to achieve this objective, the system output PDF has first been formulated analytically, which is time-variant. Then, the PDF vectorisation has been implemented to simplify the model description. Using the vector-based representation, the system identification and control design have been performed to achieve the PDF tracking. In practice, the PDF evolution is difficult to implement in real-time, thus a data-driven extension has also been discussed in this paper, where the vector-based model can be obtained using kernel density estimation (KDE) with the real-time data. Furthermore, the stability of the presented control design has been analysed, which is validated by a numerical example. As an extension, the multi-output stochastic systems have also been discussed for joint PDF tracking using the proposed algorithm, and the perspectives of advanced controller have been discussed. The main contribution of this paper is to propose: (1) a new sampling-based PDF transformation to reduce the modelling complexity, (2) a data-driven approach for online implementation without model pre-training, and (3) a feasible framework to integrate the existing control methods.
Original languageEnglish
Pages (from-to)3149-3157
Number of pages9
JournalTransactions of the Institute of Measurement and Control
Issue number14
Early online date1 Jun 2021
Publication statusPublished - 31 Oct 2021


  • stochastic distribution control
  • non-Gaussian stochastic systems
  • probability density function (PDF)
  • data-driven design
  • kernel density estimation (KDE)
  • PID controller


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