Journal
APPLIED MATHEMATICAL MODELLING
Volume 89, Issue -, Pages 792-801Publisher
ELSEVIER SCIENCE INC
DOI: 10.1016/j.apm.2020.07.051
Keywords
Time-varying delay system; Optimal state-delay control; differential evolution; Batch process
Funding
- National Natural Science Foundation of China [11771008]
- Australian Research Council [DP190103361, 201902575002]
- andtheNatural ScienceFoundation ofShandong Province, China [ZR2017MA005, ZR2019MA031]
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This paper examines an optimal control problem involving a time-varying state-delay system in the 1,3-propanediol microbial batch process, aiming to minimize errors and consider path constraints to determine unknown delay functions and kinetic parameters effectively.
In this paper, we consider optimal control problem involving a time-varying state-delay system arising in 1,3-propanediol microbial batch process. The dynamic system in this problem includes unknown time-varying delay function and unknown kinetic parameters. To optimally determine the unknown delay function and unknown kinetic parameters in the system, the weighted least-squares error between the computed values and experimental data is minimized subject to path constraints. By parameterizing the delay function with piecewise quadratic basis functions, the optimal state-delay control problem is approximated by a sequence of parameter optimization problems. Furthermore, an exact penalty method is utilized to transform these parameter optimization problems into the ones only with box constraints. On this basis, a modified differential evolution algorithm is developed to solve the resulting optimization problems. Finally, numerical results are presented to verify the effectiveness of the developed solution approach. (C) 2020 Elsevier Inc. All rights reserved.
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