# Adaptive Recursive Sliding Mode Control (ARSMC)-Based UAV Control for Future Smart Cities
## 1 Introduction
Nonlinear model identification with adaptive model predictive control using neural networks was considered in [25] and neural network observer-based control for a twin-rotor MIMO system was investigated in [26]. Learning-based fast nonlinear model predictive control to address issues of parametric uncertainty was reported in [27; 28]. One approach to address parameter uncertainty is to use a modified extended Kalman filter (EKF) to perform joint state and parameter estimation. Another method is to use the multiple model second level adaptation (MALSA) scheme [29; 30]. A discrete-time intelligent control strategy was implemented in [31], which was designed to match the behavior of the prototype. To address the nonlinear response of states following system decoupling, a robust control strategy was developed in [32]. Two types of robust control, sliding mode control (SMC) and integral SMC, were designed to overcome these nonlinearities [33; 34]. A fuzzy and LQR controller designed for decoupled systems was used to control the pitch and yaw angle over desired values based on the model. Additionally, a real-time adaptive model inversion technique utilizing an artificial neural network was proposed to control the cross-coupled dynamics of nonlinear systems in [35]. Rapid and sudden changes in rotor speeds are the primary cause of cross-coupling between pitch and yaw dynamics. However, because some states of the system cannot be measured, mathematical modeling of the system can become challenging, as the system is no longer flat. In previous research, robust generalized dynamic inversion (RGDI)-based control theory and mixed-optimization control were applied in [36; 37] to a UAV, and its performance was characterized through an experimental test of the prototype. In order to fulfill the objective, the first step involves inverting the motion equations. To simplify the model, a controller design utilizing nonlinear dynamic inversion (NDI) was implemented. To ensure system stability, calculations of controllability and observability matrices were performed, resulting in full rank matrices of order 6 \(\times\) 10 and 10 \(\times\) 6, respectively. In previous research, a real-time robust generalized dynamic inversion-based optimization was applied to the UAV, and its efficiency was evaluated through experimental testing. The issue of chattering, which can occur in higher-order complex systems with fast switching control inputs, was also addressed. The adaptive recursive sliding mode control (ARSMC) method was developed directly from the mathematical model of the system under study by introducing new variables that depend on the state variables, controlling parameters, and stabilizing functions. The stabilizing functions are used to compensate for nonlinearities in the system that can affect its operational stability. In the future of smart cities, optimizing the age and power consumption of UAVs through path learning will be crucial within the realm of Internet of Things (IoT) applications, especially for achieving efficient UAV optimization. The main objective is to design an adaptive recursive technique that incorporates adaptation laws and a recursive fast terminal sliding surface. This technique is specifically tailored for highly nonlinear and cross-coupled multiple input multiple output (MIMO) systems. The innovative approach is tested on a UAV to ensure accurate flight path tracking and stabilization. The remaining paper is organized into the mathematical modeling in two sections and the UAV stability analysis is discussed in Section 3. The recursive control design is elaborated in Section 4 and the adaptive recursive sliding mode control is explained with adaptation laws in Section 5. In Section 6, the performance of controllers is elaborated via figures. The final section provides conclusions based on a comparison of the simulation's response.