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Modelling and optimal state-delay control in microbial batch process
Applied Mathematical Modelling ( IF 5 ) Pub Date : 2021-01-01 , DOI: 10.1016/j.apm.2020.07.051
Chongyang Liu , Zhaohua Gong , Kok Lay Teo , Song Wang

Abstract 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.

中文翻译:

微生物批处理过程中的建模与优化状态延迟控制

摘要 在本文中,我们考虑了涉及 1,3-丙二醇微生物批处理过程中出现的时变状态延迟系统的最优控制问题。该问题中的动态系统包括未知的时变延迟函数和未知的动力学参数。为了最佳地确定系统中的未知延迟函数和未知动力学参数,计算值和实验数据之间的加权最小二乘误差在路径约束下被最小化。通过用分段二次基函数参数化延迟函数,最优状态延迟控制问题由一系列参数优化问题逼近。此外,使用精确惩罚方法将这些参数优化问题转换为仅具有框约束的问题。以这个为基础,改进的差分进化算法被开发来解决由此产生的优化问题。最后,给出了数值结果以验证所开发的求解方法的有效性。
更新日期:2021-01-01
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