This paper aims to determine a time-varying dilution rate of the feed medium which maximizes mean productivity while minimizing both system sensitivity and control cost in glycerol continuous culture. A multi-objective optimal control problem subjected to a nonlinear control system and its auxiliary system is proposed and transformed into a finite-dimensional large-scale multi-objective optimization problem via discretization and time-scaling transformation. A multi-objective competitive swarm optimization algorithm is constructed to solve this transformed problem based on pairwise competition, mutation operation and environment selection. The Pareto front obtained shows the distribution of the optimal target value which indicates the rationality and feasibility of the control system under the approximate optimal strategy. Numerical simulations verify the robustness of the optimal control system and the effectiveness of our numerical solution method. The value of IGD shows the good accuracy and distribution of the proposed multi-objective optimization algorithm.

本文旨在确定进料培养基的随时间变化稀释率，该稀释率可最大限度地提高平均生产率，同时最大限度地降低甘油连续培养中的系统敏感性和控制成本。提出了非线性控制系统及其辅助系统下的多目标优化控制问题，并通过离散化和时间尺度变换将其转化为有限维大规模多目标优化问题。基于成对竞争、变异操作和环境选择，构建了一种多目标竞争群优化算法来解决这一变换问题。得到的Pareto前沿显示了最优目标值的分布，表明了控制系统在近似最优策略下的合理性和可行性。数值模拟验证了最优控制系统的鲁棒性和我们数值求解方法的有效性。IGD的值表明了所提出的多目标优化算法的良好的准确性和分布。