Distributed Nonlinear Placement for Multicluster Systems: A Time-Varying Nash Equilibrium-Seeking Approach
研究多集群系统中各智能体在位置约束和网络拓扑限制下的布局问题，将其转化为时变非合作博弈，并设计分布式纳什均衡搜索算法，通过李雅普诺夫稳定性定理证明收敛性。
In this article, a class of distributed nonlinear placement problems is considered for a multicluster system. The task is to determine the positions of the agents in each cluster subject to the constraints on agent positions and the network topology. In particular, the agents in each cluster are placed to form the desired shape and minimize the sum of squares of the Euclidean lengths of the links amongst the center of each cluster and its corresponding cluster members. The problem is converted into a time-varying noncooperative game and then a distributed Nash equilibrium-seeking algorithm is designed based on a distributed observer method. A new iterative approach is employed to prove the convergence with the aid of the Lyapunov stability theorem. The effectiveness of the distributed algorithm is validated by numerical examples.