一种非线性多阶段动力系统的最优控制及数值优化

The Optimal Control and Numerical Optimization of a Class of Nonlinear Multi-Stage Dynamical System

针对间歇发酵过程的非线性多阶段动力系统,建立了以初始浓度为控制变量、以生产强度为性能指标的最优控制模型.证明了非线性多阶段动力系统的主要性质、最优控制的存在性及达到最优解的必要条件.构造了优化算法并应用于实际数据计算,其数值结果表明了本文模型与算法的有效性.

In this paper we consider a class of nonlinear multi-stage dynamical system in batch fermentation and some properties of it.Based on this system,an optimal control model is proposed where the initial state is considered as control variable and the objective is to maximize the production intensity of 1,3-Propanediol at terminal moment.We prove existence of optimal controls and obtain the necessary condition for them.Furthermore,a optimization algorithm is developed.Numerical result shows that both the nonlinear multi-stage dynamical system and the optimization algorithm are effective.