Optimal Leader–Follower Formation Control for Unmanned Aerial Vehicles Using the Multiplayer Stackelberg–Nash Game

This article addresses the optimal leader–follower formation control problem for unmanned aerial vehicles (UAVs) within a hierarchical decision-making framework. Due to the decision independence and task coupling among individuals, the Stackelberg–Nash equilibrium is employed to describe the formation-switching process. This design ultimately results in the development of a decision-making mechanism based on the multiplayer Stackelberg–Nash game (SNG). To ensure the effective execution of the closed-loop system, the saturation constraints are incorporated into the generated commands, and an auxiliary control system for command tracking is introduced. Due to the impracticality of obtaining an analytical solution to the coupled Hamilton-Jacobi-Bellman (HJB) equation in multiplayer SNG, a policy iteration–based algorithm inspired by fixed-point iteration is proposed. Subsequently, the control performance analysis demonstrates the ultimate uniform boundedness of the closed-loop system. Finally, the effectiveness and superiority of the proposed methodology are validated through simulations.