Fully probabilistic control for uncertain nonlinear stochastic systems

Ana Zafar, Randa Herzallah

    Research output: Contribution to journalArticlepeer-review


    This paper develops a novel probabilistic framework for stochastic nonlinear and uncertain control problems. The proposed framework exploits the Kullback–Leibler divergence to measure the divergence between the distribution of the closed-loop behavior of a dynamical system and a predefined ideal distribution. To facilitate the derivation of the analytic solution of the randomized controllers for nonlinear systems, transformation methods are applied such that the dynamics of the controlled system becomes affine in the state and control input. Additionally, knowledge of uncertainty is taken into consideration in the derivation of the randomized controller. The derived analytic solution of the randomized controller is shown to be obtained from a generalized state-dependent Riccati solution that takes into consideration the state-and control-dependent functional uncertainty of the controlled system. The pro-posed framework is demonstrated on an inverted pendulum on a cart problem, and the results are obtained
    Original languageEnglish
    Number of pages10
    JournalAsian Journal of Control
    Early online date11 Nov 2022
    Publication statusE-pub ahead of print - 11 Nov 2022

    Bibliographical note

    © 2022 The Authors. Asian Journal of Control published by John Wiley & Sons Australia, Ltd on behalf of Chinese Automatic Control Society. This is an open access article under the terms of the Creative Commons Attribution-NonCommercial (CC-BY-NC) License, which permits use, distribution and reproduction in any medium, provided the original work is properly cited and is not used for commercial purposes.


    • Control and Systems Engineering
    • Electrical and Electronic Engineering
    • Mathematics (miscellaneous)


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