## 2 Literature Review
The applications of FTC can be found in aerial vehicles such as quadcopters and hex copters as well. Fault detection and fault-tolerant control algorithms are suggested in [22] to address the problems of both actuator defects and disturbances in a hex copter. By utilizing sliding mode and a disturbance observer with an FDI, the motor failure is separated to resolve the one or two actuator failures. In [23], a strategy for estimating actuator faults in quadcopters operating in unknown environments is presented. An improved intermediate estimator approach, which can be used to predict actuator failures and system states, was applied to the quadcopter model to avoid the difficulty associated with solving linear matrix inequalities. A sliding mode control based on neural networks is presented in a new study for the attitude and altitude system of a quadcopter amid small perturbations [24]. In [25], the problem of fault-tolerant control for turbofan engines with actuator defects is addressed and solved using Convolution Neural Networks (CNN). During this study, a limited dimensionality is considered; hence, the proposed method is ineffective for the higher dimensionality of turbofan engines. Moreover, the CNN requires a large dataset to produce acceptable results, which makes it slow during the training stage. The existing FTCS approaches along with their shortcomings are summarized in Table 1.  
We can see from the literature that most of the work on fault detection use Kalman filters, lookup tables, linear regression, machine learning, or ANN. For malfunctioning sensors, linear regression gives less accurate sensor data, while the Kalman filters and lookup-table approaches are computationally wasteful. Because gradient descent must be done several times, the ANN-based technique necessitates forward and backward propagation. Because of this, the ANN is sluggish, and the only way to increase its speed is to utilize a GPU, which is a costly option. Hence, we propose three different approaches that can be used to estimate the values for nonlinear sensors. These approaches are PSO, \begin{table}
\begin{tabular}{c c c} \hline \hline
**Technique** & **Reference** & **Remarks** \\ \hline Kalman Filters & [7; 8; 11] & KFs use a linear state transition and measurement model, hence, less accurate for nonlinear estimation \\ \hline AIO & [9] & Inefficient in terms of computation power \\ \hline Fuzzy Logic & [10; 16; 20] & The accuracy of these systems is degraded since they frequently use incorrect data and inputs. \\ \hline Linear Regression & [12] & Less accurate estimated values \\ \hline ANN & [15; 17] & High-error data points are ignored \\ \hline CNN & [25] & Requires a large dataset \\ \hline \hline \end{tabular}
\end{table} 
Table 1: FTCS approaches and their drawbacks. GA, and NLR, which can be used to design an AFTCS for highly nonlinear sensors of an IC engine for AFR system control. During this work, the main contribution is the implementation of three estimation techniques for nonlinear sensors, given the constraint that we have a minimum dataset for the prediction of sensor values in case of a fault. The proposed techniques are implemented in such a way that the controller needs much less computational power and computational time to generate the estimated values. Finally, the performance analysis in terms of accuracy and computational power requirements is carried out to prove the superior performance of the proposed techniques. The simulations are carried out by considering an engine speed of 300 r/min, which is the implementation speed of the MATLAB model. The simulation results show the superior performance of NLR over PSO and GA and prove the superior fault tolerance performance, especially for the Manifold Absolute Pressure (MAP) sensor in terms of less oscillatory response, compared to that reported in existing literature.