@article{Wu2022, 
author = {Xiang Wu and Yuzhou Hou and Kanjian Zhang},
title = {Optimal feedback control for a class of fed-batch fermentation processes using switched dynamical system approach},
year = {2022},
journal = {AIMS Mathematics},
volume = {7},
number = {5},
pages = {9206-9231},
keywords = {optimal control, feedback control, fed-batch fermentation process, switched system, state-dependent switching},
url = {https://www.sciopen.com/article/10.3934/math.2022510},
doi = {10.3934/math.2022510},
abstract = {This paper considers an optimal feedback control problem for a class of fed-batch fermentation processes. Our main contributions are as follows. Firstly, a dynamic optimization problem for fed-batch fermentation processes is modeled as an optimal control problem of switched dynamical systems, and a general state-feedback controller is designed for this dynamic optimization problem. Unlike the existing switched dynamical system optimal control problem, the state-dependent switching method is applied to design the switching rule, and the structure of this state-feedback controller is not restricted to a particular form. Then, this problem is transformed into a mixed-integer optimal control problem by introducing a discrete-valued function. Furthermore, each of these discrete variables is represented by using a set of 0-1 variables. By using a quadratic constraint, these 0-1 variables are relaxed such that they are continuous on the closed interval    [  0  ,  1  ]. Accordingly, the original mixed-integer optimal control problem is transformed intoa nonlinear parameter optimization problem. Unlike the existing works, the constraint introduced for these 0-1 variables are at most quadratic. Thus, it does not increase the number of locally optimal solutions of the original problem. Next, an improved gradient-based algorithm is developed based on a novel search approach, and a large number of numerical experiments show that this novel search approach can effectively improve the convergence speed of this algorithm, when an iteration is trapped to a curved narrow valley bottom of the objective function. Finally, numerical results illustrate the effectiveness of this method developed by this paper.}
}