论文标题
使用基于傅立叶的预测器 - 矫正器方法，新的最佳周期性控制策略，用于化学仪的最佳定期性能
New Optimal Periodic Control Policy for the Optimal Periodic Performance of a Chemostat Using a Fourier-Gegenbauer-Based Predictor-Corrector Method
论文作者
论文摘要
以最简单的形式，化学仪的化学仪由微生物或细胞组成，这些细胞或细胞在特定的生长阶段不断生长，同时竞争单个限制营养素。在细胞生长速率，底物浓度和稀释速率的某些条件下，该理论预测和数值实验证实，定期操作的化学稳定剂表现出一种“ overyield”状态，在该状态下，在稳态操作下，性能变得更高。在本文中，我们表明，可以使用新型的积分伪光谱（IPS）方法和通过预测器 - 验证器算法组成的新型积分伪光谱方法（IPS）方法和自适应H-IPS方法来准确，有效地得出最大程度地得出Chemostat性能的最佳周期性控制策略。得出了用于构建傅里叶伪谱（PS）集成矩阵和Barycentric-Shifted Gegenbauer（SG）四倍体的新公式。介绍了对SG四元素的误差和收敛速率的严格研究，以及截断的傅立叶级数，插值操作员以及非平滑且通常T-骨化功能的集成运算符。我们还引入了一种新型的自适应方案，用于检测跳跃不连续性并从PS数据中重建分段分析功能。提出了一组广泛的数值模拟，以支持衍生的理论基础。
In its simplest form, a chemostat consists of microorganisms or cells that grow continually in a specific phase of growth while competing for a single limiting nutrient. Under certain conditions of the cell growth rate, substrate concentration, and dilution rate, the theory predicts and numerical experiments confirm that a periodically operated chemostat exhibits an "overyielding" state in which the performance becomes higher than that at steady-state operation. In this paper, we show that an optimal periodic control policy for maximizing chemostat performance can be accurately and efficiently derived numerically using a novel class of integral pseudospectral (IPS) methods and adaptive h-IPS methods composed through a predictor-corrector algorithm. New formulas for the construction of Fourier pseudospectral (PS) integration matrices and barycentric-shifted Gegenbauer (SG) quadratures are derived. A rigorous study of the errors and convergence rates of SG quadratures, as well as the truncated Fourier series, interpolation operators, and integration operators for nonsmooth and generally T-periodic functions, is presented. We also introduce a novel adaptive scheme for detecting jump discontinuities and reconstructing a piecewise analytic function from PS data. An extensive set of numerical simulations is presented to support the derived theoretical foundations.
