Optimal feedback control for a class of fed-batch fermentation processes using switched dynamical system approach

AIMS Mathematics

Xiang Wu¹  Yuzhou Hou²  Kanjian Zhang³ 

[1] 1. School of Mathematical Sciences, Guizhou Normal University, Guiyang 550001, China3. School of Electrical Engineering, Southeast University, Nanjing 210096, China;2. School of life sciences, Guizhou Normal University, Guiyang 550001, China;4. School of Automation, Southeast University, Nanjing 210096, China 5. Key Laboratory of Measurement and Control of CSE, Ministry of Education, Southeast University, Nanjing 210096, China;

关键词: optimal control;    feedback control;    fed-batch fermentation process;    switched system;    state-dependent switching;   

DOI  :  10.3934/math.2022510

来源: DOAJ

【 摘 要 】

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.

【 授权许可】

Unknown