## 1 Introduction  
The model predictive control (MPC) is a controller that predicts real-time input of the system to obtain the desired optimal output solution based on the previous and current information in each time step [1]. However, the MPC applied to nonlinear systems needs heavy computational loads [2]. To alleviate the loads, an institutive idea is to transform a nonlinear system to a linear one, and feedback linearization (FL) is a common approach to design a controller through transforming a nonlinear system into a linear system, which then can be controlled by applying linear control theory [3]. Thus, there are many papers investigating various applications combining the MPC and FL. [PERSON] and [PERSON] applied the combination to a continuous stirred tank reactor with both the input and output constraints, where the input-output feedback linearization was used to obtain a linear model and then the model was discretized to apply a discrete-time MPC [4]. [PERSON] et al. applied the combination to the outlet water temperature in a solar collector field, where the input-output FL was applied first to have a linear model and then a discrete-time filtered Smith predictor-based model predictive control algorithm was used to deal with disturbances and system uncertainties [5]. [PERSON] et al. applied the combination to a quadriceps muscle actuated knee joint, which were decoupled as inner- and outer-loop dynamics. The inner-loop dynamics control was performed by using a pole placement controller, and the outer-loop dynamics control was controlled by an input-output FL cascaded with the MPC, where the inner-loop dynamics stability was proved [6]. [PERSON] and [PERSON] applied the combination to the trajectory tracking control of a serial manipulator with a passive joint, where the underactuated system was converted by the input-output FL first, and then a discrete-time MPC. with both the input and input rate constraints, was applied [7]. [PERSON] et al. applied the combination to the temperature control of a greenhouse, where the discrete-time unscented Kalman filter was used to estimate the parameters and states of the system first, and then an input-state FL cascaded with a discrete-time MPC was applied [8]. [PERSON] et al. applied the combination to a single-link flexible joint robot and the inverted pendulum, where the nonlinear systems were transformed into linear systems by input-state FL through the Lie derivative. Besides this, the nonlinear output equations were approximated by using the finite-dimension Taylor expansion, and then the Euler backwards method was used, leading to discrete-time modes for applying the discrete-time MPC [9]. [PERSON] et al. applied the combination to the trajectory tracking control of an underactuated two-wheeled inverted pendulum vehicle, where an approximated input-output feedback linearization was used to reduce computational burden, and then a discrete-time MPC with input and state constraints was applied [10]. [PERSON] et al. applied the combination to a compliant 6-DOF robotic arm, where an inverse dynamics FL was used to obtain a discrete-time linear model, the extended Kalman filter was used to estimate the states, and a discrete-time MPC was incorporated with the model [11]. [PERSON] et al. presented the combination to a hybrid neuroprosthetic system, where an FL was used to reduce computational loads, and then an MPC was applied through a barrier cost function to deal with the nonlinear input constrains, originally converted from linear ones [12]. [PERSON] et al. presented the combination in cascade and applied it to the control of automotive fuel cell oxygen excess ratio, where an FL cascaded with a continuous-time MPC was used to perform anti-disturbance control. Besides, an extended state observer was used to overcome the slow responses and interference errors from measurements [13]. [PERSON] et al.