Journal Article

Optimal control of a switched autonomous system with time delay arising in fed-batch processes

Chongyang Liu

in IMA Journal of Applied Mathematics

Published on behalf of Institute of Mathematics and its Applications

Volume 80, issue 2, pages 569-584
Published in print April 2015 | ISSN: 0272-4960
Published online January 2014 | e-ISSN: 1464-3634 | DOI: https://dx.doi.org/10.1093/imamat/hxt053
Optimal control of a switched autonomous system with time delay arising in fed-batch processes

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In this paper, we propose a switched autonomous system with time delay to model the 1,3-propanediol (1,3-PD) production in a fed-batch process. Taking the switching instants and the terminal time as the control variables, we formulate a constrained time-delayed optimal control (CTOC) problem to optimize the 1,3-PD production process. Using a time-scaling transformation and parametrizing the switching instants into new parameters, an equivalent CTOC problem is investigated. A numerical solution method is then developed to seek the optimal control strategy. This method is based on the constraint transcription technique and the gradients of the cost functional together with those of the constraints. Numerical simulation results show that the mass of 1,3-PD per unit time at the terminal time is increased considerably compared with the experiment results.

Keywords: switched autonomous system; switching instants; time-delayed optimal control; constraint transcription; fed-batch process

Journal Article.  0 words. 

Subjects: Applied Mathematics

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