# Adaptive Recursive Sliding Mode Control (ARSMC)-Based UAV Control for Future Smart Cities
## 6 Conclusions  
We present a novel dynamic control strategy that is highly efficient and results in improved convergence time, achieved through the use of a Lyapunov stability mathematical operator. The novel dynamic recursive structure of the controller developed based on the mathematical model of the system highlights its excellent resistance against the considered varying perturbations. The effectiveness of the dynamic approach was demonstrated through worst scenario conditions, including simultaneous noise and parametric variation provided to both rotors with disturbance torque. In the future of smart cities, the optimization of UAV's age and power consumption through path learning will be a critical endeavor in the realm of Internet of Things (IoT) applications, particularly in achieving efficient UAV optimization. The primary objective of this study is to design an adaptive recursive technique, incorporating adaptation laws and a recursive fast terminal sliding surface, specifically tailored for highly nonlinear and cross-coupled multiple input multiple outputs (MIMO) systems. This innovative approach is put to the test on a UAV to ensure accurate flight path tracking and stabilization. Additionally, it is utilized to devise robust controllers that can effectively handle uncertainties in the UAV's operating environment. The control strategy implemented in this study comprised two distinct phases. The first phase involved comprehending the system's behavior, which proved to be challenging due to the presence of high coupling and disturbance torque. To address this, time-varying dynamic constraints were designed. To provide a simplified model of the TRMS, NDI is employed. However, the limitations of NDI and singularity issues were taken into account during this phase. In the second phase of the control strategy, reference trajectories were used to track the output states. To ensure robustness and stability validation against the nonlinear characteristics of the coupled system with uncertainties, sinusoidal reference tracking of states was employed. This approach aimed to address the nonlinear behavior and uncertainties within the system, thereby validating the effectiveness and reliability of the control strategy. The inclusion of a robust term in previous research controllers was developed to increase robustness against external perturbations and unmodeled states. The ARSMC method is based on the mathematical model of the TRMS system which addresses varying parametric uncertainties and loss of thrust anomalies. The controller uses an adaptive law to track the desired trajectory of the vehicle in both vertical and horizontal angles (positions). This control approach offers finite-time convergence, reduces the problem, and provides a parameter-tuning law to eliminate external perturbations. A novel reaching law based on an adaptive recursive approach with a finite-time convergence technique was  
Figure 10: Control input of yaw angle for ARSMC. used to generate a control law for stabilizing the nonlinear system. The hybrid controller was designed for full system trajectory tracking and stability in a closed-loop system and produced using hybrid Lyapunov analysis. The adaptive law was used to estimate the controller coefficients and the global stability of the closed-loop system was proved using Lyapunov analysis. Accurate fast-tracking and error convergence performance in all cases of perturbations (noise matrix, parametric disturbance) revealed the effectiveness of the applied controller. Numerical simulation was conducted to evaluate the performance of the developed control system. Based on the simulation validation, some important suggestions are provided below for control engineers to aid their understanding of the nature of control design and system behavior. * The presence of significant inherent uncertainties in the physical parameters can cause nonlinear behavior that must be addressed by precise application of recursive adaption law.