Consensus-Based Distributed Nash Equilibrium Seeking Strategies for Constrained Noncooperative Games of Clusters

This article investigates the noncooperative game of multiple clusters composed by double-integrator agents subject to set constraints. In particular, by decomposing each cluster cost function into multiple individual ones and allocating them to respective agents, the generalized Nash equilibrium (GNE) associated with the upper cluster layer is sought by the lower agent layer in terms of a hierarchical structure. A particular agent in each cluster is appointed as the messenger that is specialized in interacting with adjacent messengers from other clusters. It is first shown that the concerned seeking objective is achieved provided that the agents from the same cluster reach a consensus on their corresponding component of the GNE. Motivated by this consensus idea, a distributed seeking strategy through the intracluster interaction is first developed, which is applicable to the case where each agent has access to the information of the messengers from other clusters. Based on this result, we next consider a relaxed case where the messenger information is absent for each agent and the inter-cluster information interaction is only allowed via their messengers. Another distributed seeking strategy resorting to a distributed observer is developed via both the inter- and intra-cluster interactions. It is shown that both the developed distributed seeking strategies are capable of seeking out the concerned GNE. As extensions to the double-integrator model, we further consider two evolved models, i.e., Euler–Lagrange model and multi-integrator model. Two modified distributed seeking strategies are developed for achieving the concerned NE seeking objective. Finally, the effectiveness of the developed distributed seeking strategies is validated by an application.