Autonomous surface vehicles (ASVs) have been widely applied in ocean engineering due to their small size, low cost, and high mobility. However, more relevant encirclement control methods with many-to-one are simple and do not consider the system dynamics. This article proposes a cooperative encirclement control method for ASVs against multiple targets based on multi-agent reinforcement learning. Firstly, a dynamic target allocation algorithm is designed based on location information of both vehicles and targets, enabling vehicles to select encirclement targets in real-time according to relative distances. Subsequently, the whole encirclement process is divided into multiple stages, and a multi-stage reward function is developed based on curriculum learning to guide ASVs in completing encirclement tasks progressively, from simpler to more complex scenarios. Then, the actor and critic networks incorporating long short-term memory are constructed, respectively, and a multi-agent soft actor-critic reinforcement learning algorithm is employed to train ASVs, enhancing cooperative target encirclement maneuvers. Finally, the effectiveness and superiority of the proposed method is validated through a six-on-two encirclement simulation.

In the framework of the traditional active disturbance rejection controller (ADRC), the state error feedback utilizes estimated values from the extended state observer, which may introduce phase lag. Therefore, academic researchers have proposed a modified version called the improved linear ADRC that employs output values from the plant for state error feedback except the output value from the extended state observer. However, there is limited literature exploring the relationship between traditional linear ADRC and improved linear ADRC. To address this gap, this article establishes mathmatical relationship between traditional linear ADRC and improved linear ADRC from the generalized PID control perspective, highlighting their distinctions in the frequency domain. Compared to the traditional ADRC, the improved ADRC incorporates differential terms and offers a novel approach to realize the generalized PID control via generalized PID interpretation. And to be more specific, the improved ADRC is a new way to realize the generalized PID control by three tuned parameters, and the number of parameters of the improved ADRC is fewer than that of the generalized PID control. From the time domain, numerical simulation results demonstrate that improved ADRC exhibits superior control performance by eliminating overshoot during set value tracking processes compared to the traditional ADRC. From the disturbance rejection simulations in direct current to direct current converter (DCDC), the improved ADRC can achieve better disturbance rejection performance than the traditional ADRC. The DC bus voltage drop values of the traditional ADRC are 55.8 V and 32 V; thus, the biggest voltage drop is 55.8 V, which is 7.44 times the the improved ADRC. The voltage rise of improved ADRC can be neglected compared to the voltage rise of the traditional ADRC. From the tracking performance perspective, the time to fully reach the reference value of the traditional ADRC is about 0.3 s, and the time to fully reach the reference value of the improved ADRC is about 0.15 s.