## 1 Introduction
It operates independently of model information, possesses inherent decoupling capabilities, and is straightforward to implement in engineering applications [17; 18]. As a result, LADRC has demonstrated favorable outcomes in path-following control [19; 20; 21]. Parameter selection is a vital aspect of the controller configuration process as it directly impacts the tracking accuracy of the controller. Researchers commonly rely on manual tuning of controller parameters, which presents challenges in achieving optimal system performance. Consequently, there has been a continuous emergence of various optimization algorithms aimed at addressing this issue. For example, the heuristic algorithm, exemplified by particle swarm optimization (PSO) [22] and the genetic algorithm [23], is employed to optimize a set of fixed parameters of the controller [24; 25]. Fuzzy control and neural networks are utilized to obtain adaptive controller parameters [26; 27]. However, fuzzy control heavily relies on model information, while neural networks face challenges in making appropriate decisions based on state changes. Therefore, deep reinforcement learning (DRL) algorithms [28] that do not rely on model information and can make autonomous decisions have been promoted. DRL is a kind of algorithm that combines the computational capabilities of neural networks with the decision-making abilities of RL. Its primary objective is to train optimal decision making through continuous interactions between the agent and the environment. Currently, in the field of DRL, several algorithms have been developed, including Deep Q-Networks (DQNs) [29] and Deep Deterministic Policy Gradient (DDPG) [30]. DQNs are well suited to discrete action spaces, whereas DDPG effectively handles continuous action spaces. The Twin Delayed Deep Deterministic Policy Gradient (TD3) algorithm was developed based on DDPG with enhanced stability [31]. Current applications of the TD3 algorithm in motion control can be delineated into two main categories. The first category entails employing the TD3 algorithm directly as a controller to optimize control variables [32; 33]. The second category involves integrating the TD3 algorithm with the designed controller to enhance its intelligence and performance [34]. Comparatively, the second approach exhibits noticeable improvements in training efficiency and contributes to the advancement of intelligent control systems. Motivated by prior research, this paper presents a TD3-optimized LADRC method for the trajectory control of a powered parafoil system. The main contributions of this paper are summarized as follows:  
* A guidance law for the trajectory tracking of a powered parafoil is proposed, which effectively addresses the underactuation of the system. * Based on the guidance law, two LADRC controllers aiming to achieve 3D trajectory tracking control are designed to address challenges stemming from wind disturbances and the coupling between horizontal trajectory and altitude. * The TD3 algorithm is employed to acquire the controller's real-time parameters by leveraging the powered parafoil's flight states. The TD3-optimized LADRC was compared against the traditional LADRC control method using simulation results, demonstrating the effectiveness of the proposed approach. This paper is organized as follows: Section 2 establishes the eight-DOF model for the powered parafoil system. Section 3 introduces the guidance law and outlines the design process of the LADRC for horizontal trajectory and altitude control. The design process of the TD3-optimized LADRC is presented in Section 4. Section 5 presents the simulation results, and Section 6 concludes the paper.