Distributed Time-Varying Nash Equilibrium Searching for Nonlinear Placement of Multicluster Autonomous Aerial Vehicle Formations

This paper investigates the nonlinear placement problem for multi-cluster autonomous aerial vehicles (AAVs) formations. The AAVs in each cluster are positioned to achieve the target configuration while minimizing the sum of the squares Euclidean space distances between each center and its corresponding members of the cluster. The problem is reformulated as a time-varying noncooperative game. Firstly, considering the external disturbances of AAVs, a fast terminal sliding mode observer (FTSM) is developed to estimate the disturbance, and the convergence of the observer is proved by the Lyapunov stability theorem. Then, to search Nash equilibrium (NE) for the time-varying non-cooperative game problems, a distributed algorithm based on adaptive connectivity maintenance mechanism and gradient descent method is designed. The algorithm achieves asymptotic convergence for Nash equilibrium, which is proved by means of an iterative approach. Finally, the algorithm's effectiveness is demonstrated through a simulation example.