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Indexed by:期刊论文

Date of Publication:2014-11-01

Journal:JOURNAL OF PROCESS CONTROL

Included Journals:SCIE、EI、Scopus

Volume:24

Issue:11

Page Number:1740-1746

ISSN No.:0959-1524

Key Words:Nonlinear time-delay system; Batch culture; Optimal control; Continuous state inequality constraint; Modified Nelder-Mead method

Abstract:In this paper, an enzyme-catalytic nonlinear time-delay system is investigated to describe the batch culture of glycerol to 1,3-propanediol (1,3-PD) by Klebsiella pneumoniae (K. pneumoniae), in which glycerol and 1,3-PD are assumed to pass the cell membrane by passive diffusion coupled with facilitated transport. The existence, uniqueness, boundness of solutions of the system and continuity of solutions with respect to the uncertain parameter appeared in the studied system are also discussed. The purpose of this article is to maximize the productivity of 1,3-PD at terminal time by controlling the initial value of the state vector and terminal time. With this in mind, taking the productivity of 1,3-PD at terminal time as the cost function and the initial concentration of biomass, glycerol, and terminal time as the control vectors, we firstly propose an optimal control model subject to the time-delay system and continuous state inequality constraints. To seek the optimal productivity of 1,3-PD at terminal time and the optimal control, a modified Nelder-Mead algorithm involved with the constraint transcription and smoothing techniques is then developed. Finally, the numerical results illustrate the appropriateness of the enzyme-catalytic nonlinear dynamic system and the validity of the optimization algorithm. (C) 2014 Elsevier Ltd. All rights reserved.