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Recent advances in unmanned aerial vehicle (UAV) technology have revolutionized various industries, finding applications in embedded systems, autonomy, control, security, and communication. Autonomous UAVs are distinguished by their ability to make informed decisions, anticipate potential scenarios, and learn from past experiences with the help of AI algorithms. This paper examines a practical monitoring system with an autonomous UAV, a charging station, and multiple targets that move randomly within a defined mission area. The mission area is divided into zones, and the UAV navigates through these zones efficiently. The primary objective is to maximize the probability of detecting targets, considering constraints such as limited battery life and charging station location. This challenge is initially framed as a search benefit maximization problem and subsequently reformulated as a Markov Decision Process (MDP) problem. To address the MDP formulation, we introduce a reinforcement learning (RL)-based approach that enables the UAV to comprehend unpredictable multi-target movements autonomously. The placement of the charging station in the proposed system is determined using the optimal median approach. The simulation results demonstrate that the proposed RL-based detection system significantly outperforms the reference systems in terms of detection rate and convergence. [ABSTRACT FROM AUTHOR]