2022/07/10 by Kareem T. Elgindy, Elgindy, Kareem T. · 2 citations
Agricultural and Biological Sciences · Biochemistry, Genetics and Molecular Biology · Chemistry · #FOS: Mathematics #Food Drying and Modeling #Magnetic and Electromagnetic Effects #Numerical Analysis (math.NA) #Optimization and Control (math.OC) #thermodynamics and calorimetric analyses
paper · pdf · doi:10.48550/arxiv.2207.04561
openalex publication_date 2022/07/10 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.