## Abstract  
In this paper, an observer-based robust fault-tolerant predictive control (ORFTPC) strategy is proposed for Linear Parameter-Varying (LPV) systems subject to input constraints and sensor failures. The main objective of this work is to establish a real observer based on a virtual observer to be used to estimate both states and sensor failures of the system. The proposed virtual observer is employed to improve the observation precision and reduce the impacts of the sensor faults and the external disturbances in the LPV systems. In addition, a real observer is proposed to overcome the virtual observer margins and to ensure that all states and sensor faults of the system are properly estimated, without the need for any fault isolation modules. The proposed solution demonstrates that, using both observers, a robust fault-tolerant predictive control is established via the Lyapunov function. Moreover, sufficient stability conditions are derived using the Lyapunov approach for the convergence of the proposed robust controller. Furthermore, the proposed approach simultaneously computes the gains of the real observer and the controller from a linear matrix inequality (LMI), which is deduced from the estimation errors. Finally, the performance of the proposed approach is investigated by a simulation example of a quarter-vehicle model, and the simulation results under a sensor fault illustrate the robustness and performance of the proposed method. 1 Laboratory of ISMA, Department of Mechanical Engineering, Faculty of Sciences and Technology,  
Abbes Laghrouv University, Khenelela 40004, Algeria; [EMAIL_ADDRESS]  
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to reduce the faults' impacts on the control system [5; 6]. As a result, the AFTC adjusts its structure or parameters based on the estimated faults obtained by the fault detection and identification (FDI) block, and the proposed AFTC design manipulates the estimated faults to maintain better performance in terms of stability, robustness, and fault tolerability [7]. Linear Parameter-Varying (LPV) modeling approaches have received considerable attention over the past three decades in modeling and control areas. This is due to their efficiency in dealing with tractable mathematical descriptions for relatively complex nonlinear systems. One of the main types of LPV systems is the polytopic form, which allows the system to be described as a form of a convex combination of sub-models, and these sub-models are defined by the vertices of a convex polytope. As a result, the sub-models are combined to form the LPV model of the system by convex weighing functions, resulting in the global model of the system. Many nonlinear systems have been successfully represented by LPV models [8; 9; 10]. Recently, many researchers have been attracted by the theory of solving nonlinear systems subject to faults based on the LPV representations, and many research papers have been published in the last few years. [PERSON] and [PERSON] [11] investigated robust H-1 filtering for singular LPV systems subject to time-varying delays, while the states of the system were estimated but without any FDI purposes. [PERSON] et al. [12] proposed an approach to deal with polytopic models with unknown inputs and used a proportional integral observer for fault detection and isolation. [PERSON] et al. [13] proposed and investigated an adaptive fault diagnosis observer-based approach for regular LTI systems to deal with actuator faults. Although this proposed approach can be easily modified to deal with LPV systems, unfortunately, the methodology itself can only detect and estimate constant actuator faults. [PERSON] et al. [14] proposed a technique for LPV systems in which an observer-based approach is synthesized to estimate polymer electrolyte membrane (PEM) system states while varying parameters were planned with state variables.