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Parameter identification for a nonlinear enzyme-catalytic dynamic system with time-delays

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Abstract

In this paper, we consider a nonlinear enzyme-catalytic dynamical system with uncertain system parameters and state-delays for describing the process of batch culture. Some important properties of the time-delay system are discussed. Taking account of the difficulty in accurately measuring the concentrations of intracellular substances and the absence of equilibrium points for the time-delay system, we define quantitatively biological robustness of the intracellular substance concentrations for the entire process of batch culture to identify the uncertain system parameters and state-delays. Taking the defined biological robustness as a cost function, we establish an identification model subject to the time-delay system, continuous state inequality constraints and parameter constraints. By a penalty approach, this model can be converted into a sequence of nonlinear programming submodels. In consideration of both the difficulty in finding analytical solutions and the complexity of numerical solution to the nonlinear system, based on an improved simulated annealing, we develop a parallelized synchronous algorithm to solve these nonlinear programming submodels. An illustrative numerical example shows the appropriateness of the optimal system parameters and state-delays as well as the validity of the parallel algorithm.

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Acknowledgments

This work was supported by the National Natural Science Foundation of China (Grant Nos. 11171050, 11101262 and 11371164), the National Natural Science Foundation for the Youth of China (Grant Nos. 11301051, 11301081 and 11401073) and Provincial Natural Science Foundation of Fujian (Grant Nos. 2014J05001).

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Authors and Affiliations

  1. School of Mathematical Sciences, Dalian University of Technology, Dalian, People’s Republic of China

    Jinlong Yuan, Lei Wang, Xu Zhang & Enmin Feng

  2. School of Energy and Power Engineering, Dalian University of Technology, Dalian, People’s Republic of China

    Jinlong Yuan & Hongchao Yin

  3. School of Life Science and Biotechnology, Dalian University of Technology, Dalian, People’s Republic of China

    Zhilong Xiu

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  1. Jinlong Yuan
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Correspondence to Jinlong Yuan.

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Yuan, J., Wang, L., Zhang, X. et al. Parameter identification for a nonlinear enzyme-catalytic dynamic system with time-delays. J Glob Optim 62, 791–810 (2015). https://doi.org/10.1007/s10898-014-0245-4

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