Indexed by:期刊论文

Date of Publication:2009-11-01

Journal:JOURNAL OF INDUSTRIAL AND MANAGEMENT OPTIMIZATION

Included Journals:SCIE、Scopus

Volume:5

Issue:4

Page Number:835-850

ISSN No.:1547-5816

Key Words:Nonlinear multistage system; Optimal control; Control parametrization; Fed-batch culture; Improved PSO algorithm

Abstract:In this paper, we propose a new controlled multistate system to formulate the fed-batch culture process of glycerol bio-dissimilation to 1,3-propanediol (1,3-PD) by regarding the feeding rate of glycerol as a control function. Compared with the previous systems, this system doesn't take the feeding process as an impulsive form, but a time-continuous process, which is much closer to the actual culture process. Some properties of the above dynamical system are then proved. To maximize the concentration of 1,3-PD at the terminal time, we develop an optimal control model subject to our proposed controlled multistage system and continuous state inequality constraints. The existence of optimal control is proved by bounded variation theory. Through the discretization of the control space, the control function is approximated by piecewise constant functions. In this way, the optimal control model is approximated by a sequence of parameter optimization problems. The convergence analysis of this approximation is also investigated. Furthermore, a global optimization algorithm is constructed on the basis of the above descretization concept and an improved Particle Swarm Optimization (PSO) algorithm. Numerical results show that, by employing the optimal control policy, the concentration of 1,3-PD at the terminal time can be increased considerably.