We introduce a mathematical model for the composting process in biocells. The model includes several phenomena, like the aerobic biodegradation of the soluble substrate by means of a bacterial population, the hydrolysis of insoluble substrate, and the biomass decay. We investigate the best strategies to reduce substrate components in minimal time by controlling the effects of cell oxygen concentration on the degradation phenomenon. It is shown that singular controls are not optimal for this model and the optimal control time profiles are of bang or bang‐bang type. The occurrence of switching curves is discussed. In the case of a bang‐bang control we prove that optimal control profiles have a unique switching time and the corresponding switching curve is determined.

中文翻译：

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生物细胞堆肥厂中有氧降解过程的最小时间控制问题

我们介绍了生物细胞堆肥过程的数学模型。该模型包括多种现象，例如通过细菌种群对可溶性底物进行好氧生物降解，不溶性底物的水解以及生物量的降解。我们研究了通过控制细胞氧浓度对降解现象的影响，在最短时间内减少底物成分的最佳策略。结果表明，对于该模型，奇异控制不是最优的，最优控制时间曲线是爆炸或爆炸类型的。讨论了切换曲线的出现。在爆炸控制的情况下，我们证明了最佳控制曲线具有唯一的开关时间，并确定了相应的开关曲线。