A CLASS OF NONLINEAR MULTISTAGE DYNAMICAL SYSTEM AND ITS OPTIMAL CONTROL

作者：Wang Huiyuan^*; Feng Enmin; Xiu Zhilong

来源：Rocky Mountain Journal of Mathematics, 2008, 38(5): 1745-1760.

DOI：10.1216/RMJ-2008-38-5-1745

• Bio-dissimilation
• nonlinear multistage dynamical system
• batch fermentation
• optimal control

In this paper we study a nonlinear multistage dynamical system as well as its optimal control. Specifically, based on the batch fermentation including three different phases of bio-dissimilation of glycerol to 1,3-Propanediol by Klebsiella pneumonicae, the nonlinear multi-stage dynamical system is proposed. Then we discuss several properties of this nonlinear system. In order to optimize the initial state such that; the concentration of 1,3-Propanediol at terminal time is as large as possible, an optimal control model is established. We investigate the existence of the local maximizer. Furthermore, by using the infinite-dimensional optimization principle, the necessary condition for the optimal control problem is obtained. Finally, employing some properties of the feasible region, infinite-dimensional constraints can be transformed into finite-dimensional constraints.

• 出版日期2008
• 单位大连理工大学