## 1 Introduction  
The implementation of modern and sophisticated implantable rotary blood pumps (IRBPs) to treat patients with heart failure (HF) is still under development [1, 2]. These devices are utilized to maintain the physiological perfusion of the body on both sides (left and right) of the heart. However, 75% of HF is caused by a predominant left ventricular failure. Therefore, IRBPs are increasingly used for patients with chronic heart disease; they require a complex control technique [3]. The traditional control methods used by these devices have different limitations when adjusting the pump speed under various physiological conditions of the heart [4]. In addition, the implantation of additional sensors is not desired because of thrombi; it also decreases the dependability of the system, raises the cost, and requires constant calibration due to measurement drifts [5]. In the literature, several modern control mechanisms have recently been developed to regulate or track the specified set point of IRBPs [6, 7, 8]. A few of these methods use sensors such as the flow or pump differential pressure to adapt the pump speed by enhancing the mode of operation [9, 10]. Other methods implement sensorless techniques to estimate the heart pump parameters [11, 12]. However, to improve the functionality of the settings of the pump and to enhance the reliability of the pump, an advanced physiological controller for IRBPs needs to be implemented [12]. The status of patients with HF can be professionally monitored and controlled using different control methods. For instance, [PERSON] et al. [8] proposed and implemented an extremum-seeking control algorithm to regulate the pump flow based on the amplitude of the limit cycle of the heart. This method was evaluated using an in silico model; the results demonstrated that the control method successfully maintained the mean arterial pressure whilst preventing suction. In a different work, [PERSON] et al. [11] developed an intelligent approach to regulate the pump flow in a HeartWare HVAD pump. This method was implemented using a deep convolutional neural network (CNN) to estimate the preload parameter for the patient. Computer simulations were used to evaluate the proposed controller and the results showed that the method accurately regulated the pump speed in a real-time mode. The polynomial control (PC) technique has also been suggested and used by researchers to control IRBPs. In a recent study, the PC was utilized to maintain the average arterial pressure at a particular reference value. This control method regulated the pump differential pressures in each cardiac cycle. The parameters were optimized and calculated using an internal point with minimization. The process was operated under a human heartbeat using an electrocardiogram (ECG) heartbeat algorithm. The method was evaluated using a mathematical simulation of the pediatric cardiovascular system (CVS) and a pediatric pump was applied. The computer simulation results were in agreement with the clinical status of the patient [13]. A classical control method has also been proposed and successfully implemented to drive IRBPs. In this context, a feedback control (FBC) was proposed to predict stochastic models for patients with HF under different physiological conditions. The control algorithm was developed and tested to prevent suction in three scenarios [14]. In addition, a full-state FBC method has also been developed and evaluated. For instance, [PERSON] et al. [3] used the FSC technique to regulate the pulsatility of the pump flow. This method was implemented to emulate the Frank-Starling mechanism to prevent suction or overperfusion. The controller was evaluated using the cardiovascular system (CVS) of a lumped parameter model based on two scenarios. The results demonstrated that the controller was able to maintain the physiological perfusion within clinical conditions. In addition, the nonlinear application of fuzzy logic control (FLC) has been developed for RBP systems. For instance, [PERSON] et al.