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Distributionally robust parameter identification of a time-delay dynamical system with stochastic measurements

机译：具有随机测量的时滞动力系统的分布鲁棒参数辨识

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摘要

In this paper, we consider a parameter identification problem involving a time-delay dynamical system, in which the measured data are stochastic variable. However, the probability distribution of this stochastic variable is not available and the only information we have is its first moment. This problem is formulated as a distributionally robust parameter identification problem governed by a time-delay dynamical system. Using duality theory of linear optimization in a probability space, the distributionally robust parameter identification problem, which is a bi-level optimization problem, is transformed into a single-level optimization problem with a semi-infinite constraint. By applying problem transformation and smoothing techniques, the semi-infinite constraint is approximated by a smooth constraint and the convergence of the smooth approximation method is established. Then, the gradients of the cost and constraint functions with respect to time-delay and parameters are derived. On this basis, a gradient-based optimization method for solving the transformed problem is developed. Finally, we present an example, arising in practical fermentation process, to illustrate the applicability of the proposed method. (C) 2018 Elsevier Inc. All rights reserved.
机译：在本文中，我们考虑一个涉及时滞动力系统的参数识别问题，其中测得的数据是随机变量。但是，该随机变量的概率分布不可用，唯一的信息就是它的第一刻。这个问题被表述为由时滞动力系统控制的分布鲁棒的参数识别问题。利用概率空间中线性优化的对偶理论，将分布稳健的参数识别问题（即双层优化问题）转化为具有半无限约束的单级优化问题。通过应用问题变换和平滑技术，通过平滑约束对半无限约束进行逼近，并建立了平滑逼近方法的收敛性。然后，得出关于时间延迟和参数的成本和约束函数的梯度。在此基础上，提出了一种基于梯度的优化方法来求解变换问题。最后，我们给出一个在实际发酵过程中产生的例子，以说明所提出方法的适用性。 （C）2018 Elsevier Inc.保留所有权利。

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  • 来源
    《Applied Mathematical Modelling》 |2019年第5期|685-695|共11页
  • 作者

    Gong Zhaohua; Liu Chongyang; Teo Kok Lay; Sun Jie;

  • 作者单位

    Shandong Inst Business & Technol, Sch Math & Informat Sci, Yantai 264005, Peoples R China;

    Shandong Inst Business & Technol, Sch Math & Informat Sci, Yantai 264005, Peoples R China|Curtin Univ, Sch Elect Engn Comp & Math Sci, Perth, WA 6845, Australia;

    Curtin Univ, Sch Elect Engn Comp & Math Sci, Perth, WA 6845, Australia|Tianjin Univ Finance & Econ, Coordinated Innovat Ctr Computable Modeling Manag, Tianjin 300222, Peoples R China;

    Curtin Univ, Sch Elect Engn Comp & Math Sci, Perth, WA 6845, Australia;

  • 收录信息 美国《科学引文索引》(SCI);美国《工程索引》(EI);
  • 原文格式 PDF
  • 正文语种 eng
  • 中图分类
  • 关键词

    Parameter identification; Distributionally robust optimization; Duality theory; Time-delay system; Semi-infinite optimization;

    机译：参数辨识;分布鲁棒优化;对偶理论;时滞系统;半无限优化;

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