## 1 Introduction
### Related Work  
Symbolic approaches have been effectively utilized in discrete control synthesis in various domains. [PERSON]. [27; 28] achieved significant results in the energy efficiency of hardware circuits using symbolic DCS. [PERSON]. [29; 30] applied it to electric vehicles and power grids, obtaining notably good results compared to other popular methods. Similarly, [PERSON]. [31] addressed the path problem for CNC machines in multi-pocket milling. Lastly, [PERSON]. [32; 33] demonstrated that, for robotic systems and UAVs, path problems are better solved compared to alternative machine learning approaches. The control strategies of UAVs are involved in many studies. The objective of [34] is to conduct a comparative analysis of two distinct control methodologies, PID and FOPID, in the context of a nonlinear, underactuated quadcopter system. The dynamics of the quadcopter's movement are examined to establish a mathematical model. Subsequently, the mathematical model is simulated using Simulink of MATLAB 2021a software. The effectiveness of the PID and FOPID control techniques in stabilizing the quadcopter's motion is evaluated, and the outcomes are juxtaposed to ascertain the superior control strategy. [PERSON]. [35] examines quadrotors which are widely used due to their cost effectiveness and ease of construction, thanks to their efficiency. The controller system utilized for the quadrotors is the PID-based plant model. However, the PID controller has limitations in achieving precise position control. To address these limitations, the performance of the PID controller is compared to that of a FOPID controller through simulation. The FOPID controller is designed to fine-tune the PID plant model to enhance drone stabilization and minimize disruptions during flight. Following fine-tuning, the proposed FOPID controller achieved a lower settling time, better disturbance rejection, and improved set point tracking compared to the PID controller. This performance enhancement is also evident when dealing with complex inputs, such as sinusoidal signals. In many studies, the autonomy and control capabilities of the UAVs are investigated together. Ref. [36] presents a thorough investigation into improving the autonomy and control capabilities of quadcopters. The main focus is on developing and implementing three conventional control methods to improve the dynamic behavior of quadcopter UAVs: the PID controller, the sliding mode controller, and the FOPID controller. These commonly known controllers are utilized to provide the desired dynamic output and stability during the flight of the quadcopter. Additionally, Dyna-Q learning, which is an obstacle avoidance method, is integrated into the control system. Using MATLAB, the quadcopter navigated autonomously in complex environments by avoiding the obstacles through decision making and real-time learning processes. The performance of the various control methods, including Dyna-Q learning, were compared through the experiments and evaluations performed in MATLAB. The comprehensive analysis provides significant solutions to optimize the flight stability in various real-world missions. In the rapidly evolving field of autonomous UAVs, various control strategies for UAV systems have been extensively studied. The conventional PID controllers are widely considered at different stages of the control loop. Despite the enhanced flexibility offered by fractional order PID (FOPID) controllers compared to their integer-order counterparts (IOPID), their adoption remains cautious due to heightened computational demands during tuning and challenges in achieving precise real-time implementation. Addressing these concerns, Ref. [37] introduces a Surrogate-Based Analysis and Optimization (SBAO) technique tailored for higher order approximations of FOPID controllers. The efficacy of the proposed method is validated through two case studies.