Distributed Generalized Nash Equilibrium Seeking for Constrained N-Cluster Games with Second-Order Dynamics

This paper studies N-cluster games with secondorder dynamics, wherein the players’ decisions are restricted by local set constraints and nonlinear coupled inequality constraints. The presence of second-order dynamics coupled with constraints leads to difficulties in the design and analysis of generalized Nash equilibrium (GNE) seeking algorithms, since it may be impossible to directly determine the decisions of players based on their control inputs. To facilitate the autonomous execution of N-cluster game tasks through secondorder players, by employing state feedback, projection, primaldual, dynamic average consensus, and passivity methods, a distributed algorithm is proposed to find the variational GNE of the studied games, under which the players’ decisions can satisfy the set constraints all the time. Additionally, the algorithm’s convergence is rigorously analyzed, and its efficacy is validated by a simulation example.