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    Robust optimization for nonlinear time-delay dynamical system of dha regulon with cost sensitivity constraint in batch culture

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    Access Status
    Open access
    Authors
    Yuan, J.
    Zhang, X.
    Liu, Chongyang
    Chang, L.
    Xie, J.
    Feng, E.
    Yin, H.
    Xiu, Z.
    Date
    2016
    Type
    Journal Article
    
    Metadata
    Show full item record
    Citation
    Yuan, J. and Zhang, X. and Liu, C. and Chang, L. and Xie, J. and Feng, E. and Yin, H. et al. 2016. Robust optimization for nonlinear time-delay dynamical system of dha regulon with cost sensitivity constraint in batch culture. Communications in Nonlinear Science and Numerical Simulation. 38: pp. 140-171.
    Source Title
    Communications in Nonlinear Science and Numerical Simulation
    DOI
    10.1016/j.cnsns.2016.02.008
    ISSN
    1007-5704
    School
    Department of Mathematics and Statistics
    URI
    http://hdl.handle.net/20.500.11937/33364
    Collection
    • Curtin Research Publications
    Abstract

    Time-delay dynamical systems, which depend on both the current state of the system and the state at delayed times, have been an active area of research in many real-world applications. In this paper, we consider a nonlinear time-delay dynamical system of dha-regulon with unknown time-delays in batch culture of glycerol bioconversion to 1,3-propanediol induced by Klebsiella pneumonia. Some important properties and strong positive invariance are discussed. Because of the difficulty in accurately measuring the concentrations of intracellular substances and the absence of equilibrium points for the time-delay system, a quantitative biological robustness for the concentrations of intracellular substances is defined by penalizing a weighted sum of the expectation and variance of the relative deviation between system outputs before and after the time-delays are perturbed. Our goal is to determine optimal values of the time-delays. To this end, we formulate an optimization problem in which the time delays are decision variables and the cost function is to minimize the biological robustness. This optimization problem is subject to the time-delay system, parameter constraints, continuous state inequality constraints for ensuring that the concentrations of extracellular and intracellular substances lie within specified limits, a quality constraint to reflect operational requirements and a cost sensitivity constraint for ensuring that an acceptable level of the system performance is achieved. It is approximated as a sequence of nonlinear programming sub-problems through the application of constraint transcription and local smoothing approximation techniques. Due to the highly complex nature of this optimization problem, the computational cost is high. Thus, a parallel algorithm is proposed to solve these nonlinear programming sub-problems based on the filled function method. Finally, it is observed that the obtained optimal estimates for the time-delays are highly satisfactory via numerical simulations.

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