Adaptive Optimal Surrounding Control of Multiple Unmanned Surface Vessels via Actor-Critic Reinforcement Learning.

In this article, an optimal surrounding control algorithm is proposed for multiple unmanned surface vessels (USVs), in which actor-critic reinforcement learning (RL) is utilized to optimize the merging process. Specifically, the multiple-USV optimal surrounding control problem is first transformed into the Hamilton-Jacobi-Bellman (HJB) equation, which is difficult to solve due to its nonlinearity. An adaptive actor-critic RL control paradigm is then proposed to obtain the optimal surround strategy, wherein the Bellman residual error is utilized to construct the network update laws. Particularly, a virtual controller representing intermediate transitions and an actual controller operating on a dynamics model are employed as surrounding control solutions for second-order USVs; thus, optimal surrounding control of the USVs is guaranteed. In addition, the stability of the proposed controller is analyzed by means of Lyapunov theory functions. Finally, numerical simulation results demonstrate that the proposed actor-critic RL-based surrounding controller can achieve the surrounding objective while optimizing the evolution process and obtains 9.76% and 20.85% reduction in trajectory length and energy consumption compared with the existing controller.