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Optimal parameter selection for nonlinear multistage systems with time-delays

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  • Chongyang Liu
  • Ryan Loxton
  • Kok Teo

Abstract

In this paper, we consider a novel dynamic optimization problem for nonlinear multistage systems with time-delays. Such systems evolve over multiple stages, with the dynamics in each stage depending on both the current state of the system and the state at delayed times. The optimization problem involves choosing the values of the time-delays, as well as the values of additional parameters that influence the system dynamics, to minimize a given cost functional. We first show that the partial derivatives of the system state with respect to the time-delays and system parameters can be computed by solving a set of auxiliary dynamic systems in conjunction with the governing multistage system. On this basis, a gradient-based optimization algorithm is proposed to determine the optimal values of the delays and system parameters. Finally, two example problems, one of which involves parameter identification for a realistic fed-batch fermentation process, are solved to demonstrate the algorithm’s effectiveness. Copyright Springer Science+Business Media New York 2014

Suggested Citation

  • Chongyang Liu & Ryan Loxton & Kok Teo, 2014. "Optimal parameter selection for nonlinear multistage systems with time-delays," Computational Optimization and Applications, Springer, vol. 59(1), pages 285-306, October.
    • Handle: RePEc:spr:coopap:v:59:y:2014:i:1:p:285-306
    DOI: 10.1007/s10589-013-9632-x
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    References listed on IDEAS

    as
    1. Jianjun Shi & Shiyu Zhou, 2009. "Quality control and improvement for multistage systems: A survey," IISE Transactions, Taylor & Francis Journals, vol. 41(9), pages 744-753.
    2. Zhi Guo Feng & Kok Lay Teo, 2010. "Optimal Feedback Control for Stochastic Impulsive Linear Systems Subject to Poisson Processes," Springer Optimization and Its Applications, in: Altannar Chinchuluun & Panos M. Pardalos & Rentsen Enkhbat & Ider Tseveendorj (ed.), Optimization and Optimal Control, pages 241-258, Springer.
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    Cited by:

    1. Guanming Cheng & Lei Wang & Ryan Loxton & Qun Lin, 2015. "Robust Optimal Control of a Microbial Batch Culture Process," Journal of Optimization Theory and Applications, Springer, vol. 167(1), pages 342-362, October.

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