Two-layer leader-follower optimal affine formation maneuver control for networked unmanned surface vessels with input saturations

This article studies the two-layer leader-follower optimal affine formation maneuver (AFM) control problem for multiple unmanned surface vessels (USV). The basic idea of the developed two-layer control framework is to realize the time-varying formation for the leader group in advance, and then let the follower USVs agilely respond to the target formation affinely localized by leaders. To realize this goal, a time-varying formation reference system is first synthesized to describe leaders' target formation in the affine map of the nominal configuration. The reference system is set up by virtual vessel velocity command and unrotated geometric command, which make it possesses an intuitive application structure for operators to plan AFM commands in real-time sensed surrounding environments. Then, by means of optimized backstepping design and the adaptive dynamic programming technique, actor-only reinforcement learning controllers are established for USVs in both two layers to realize the optimal target formation tracking objective. For the proposed optimal controllers, the persistent excitation condition that is required by common optimal control schemes is also removed, which endows the presented scheme with lower computational complexity. Finally, theoretical analysis and simulation results illustrate the closed-loop stability and the effectiveness of the presented scheme.