## 1 Introduction
The p53 pathway's dynamic response is controlled by a complex network of feedback loops. The first investigations were conducted with the goal of monitoring the behaviors at the level of the cell population [18; 19]. However, it was later discovered that monitoring the dynamics of a population can obscure the true behavior of individual cells within the population. Therefore, by analyzing a fluorescence-tagged protein, it is possible to deduce the hidden dynamics of a particular cell [20]. The p53-MDM2 loop may show a variety of dynamic response patterns, which vary depending on the input. In general, these patterns may be classified as being oscillatory or sustained [21]. In the event of less severe DNA damage, it has been shown that p53 will start oscillations. Further, the oscillatory behavior may be divided into categories, namely: digital pulses and oscillations with damped or sustained amplitude. It is important to note that the frequency of the pulses is directly related to the amount of DNA damage, but the width of the pulse and its magnitude remain constant [22]. The pulsing p53 gene is often linked with DNA synthesis or apoptosis, respectively. The condition of the DNA is checked after every pulse of about 6 h. In the event that the DNA is fixed, the oscillating p53 is killed, and the cell cycle activity is resumed. The continuous p53 response is triggered as a result of severe DNA damage. The magnitude of the reaction and its width are both in direct proportion to the degree of the damage that has occurred. In this particular instance, the expressed genes result in cell death [22; 23]. It is clear that in the event of significant DNA mutation, p53 does not allow the cell to recover in enough time to repair the damage and, instead, kills the cell instantly. Statistical frameworks enable us to obtain a better understanding of the network structure, develop new ideas, and explore unknown areas. The majority of modeling research on the p53 pathway has focused on the dynamics of p53 and MDM2 [24]. Mathematical models including continuous time, discrete time, and delayed time are used in the literature [25; 26; 27]. Systems biology (SB) has traditionally been used to analyze and predict the response of complex biological systems. Recently, SB has been utilized as a valuable tool for accurately directing therapeutic treatments in complex biological networks when combined with control theory. While considerable improvements have been achieved in medication delivery to cardiovascular systems [28], blood pressure management [29], tumor chemotherapy [30], anesthetic drug delivery [31], diabetic control [32], Parkinson's tremor [33], and HIV/AIDS control [34; 35], there have also been notable setbacks. The use of control engineering in cancer therapy is a relatively recent field of study. The primary goal of cancer therapy is to achieve complete remission of malignant cells in the shortest amount of time possible while preserving the patient's overall health. While chemotherapy, radiation, and surgical procedures are effective treatments, these operations may have a negative impact on the patient's quality of life [36]. The current research pattern is moving away from traditional methods of analysis and control and toward in silico methods. There is a compelling need to utilize in silico simulations to execute medication design utilizing control theory in order to improve patient outcomes. The control guarantees that the treatment is administered and that the medication is scheduled. Even the most advanced numerical modeling of bio-systems does not always yield an accurate outcome. Consequently, it is necessary to perform the desired task by developing a control system that can cope with the imprecisions and uncertainties inherent in the modeling process. The p53 pathway has been the subject of research in a handful of model-based control methods in the literature. It was shown in [37] how to construct flatness-based control for sustaining a target level of p53 by making use of p53 models and its associated pathways.