## 1 Introduction  
### Current State and Motivation  
Recently, there has been an explosive growth in the research, development, and sales of new products based on Bioprocess Engineering. Bioprocessing is an essential part of many food, chemical, and pharmaceutical industries. Bioprocess operations make use of microbial, animal and plant cells and components of cells such as enzymes to manufacture new products and destroy harmful waste [1]. Bioprocess Engineering's central problems derive from a lack of knowledge concerning the intrinsic behaviour of cells and proteins, non-linear dynamic behaviour, and time-variant features [2]. With globalisation, market competitiveness, and environmental concerns, a real need has appeared for high-quality products, low cost, and low emission of pollutants. This is the main reason for the recent advance in the research of new methodologies and conceptions about bioprocess development and bioprocess control in all areas. The primary bioprocess used for application in several biotechnology branches is the fermentation process. Industrial fermentation is executed mainly in bioreactors. Regarding the feeding strategy,the bioreactors can be classified as continuous-, batch-, or fed-batch bioreactors [3]. Most industrial bioreactors operate in batch or fed-batch mode to allow more efficient media utilisation and to avoid sterility problems caused by continuous liquid removal. Despite frequently encountered open-loop strategies in the industrial usage of bioreactors, the common difficulty of these techniques is that no compensation is made for random disturbances during the process operation. For optimal production in bioreactors, the growth of microorganisms should be controlled for optimal production in bioreactors. Control can be realised in bioreactors of different types by changing the input variables, such as respiration, fermentation temperature, substrate concentration, nutrient flow rates, pH value, and stirrer speed. Reliable and accurate on-line sensors that allow real-time monitoring of the process state and control realisation are only available for some of a bioreactor's variables, such as temperature, pH, O\({}_{2}\), and \(\gamma\)[4]. Therefore, one or more of these variables are chosen as the output variables, which are regulated according to defined set-points, or tracked to reference trajectories. bioreactors normally include a measurement system for inlet gas flow rate, stirrer speed, temperature, pH, and dissolved oxygen. In most cases, dissolved oxygen is monitored, as one of the significant parameters in an aerobic fermentation process. Its control is difficult to achieve, due to variations in process dynamics during both batch and fed-batch processes [5]. Recent advances in accurate on-line measurement technology have resulted in model-based control strategies that offer the potential for improved bioreactor performance. For each microorganism and target product, there exists an optimal physiological state or trajectory, where the target product is produced at the maximum quantity and at a satisfactory quality. The goal of the control is to maintain the biochemical processes at that optimal state during the fermentation process [6]. Sometimes, the optimal trajectory approaches the critical one, which is unstable, making it difficult to control. It is extremely important to incorporate mathematical descriptions or dynamics of specific biochemical processes in monitoring and control algorithms [7]. The complexity of the underlying biochemical processes varies in an unpredictable manner. Additionally, process conditions change continuously due to culture ageing, spontaneous mutations, wall growth, and different external disturbances. For such systems, accurate process models are rarely available. For the batch and fed-batch bioreactors, a control objective is to maximise the quantity of the desired product at the end of the batch and minimise the duration of the fermentation process.