Dynamic Nash Equilibrium Seeking for Constrained Noncooperative Game of Open Multiagent Systems

Open multiagent systems (OMASs) feature a dynamic structure with agents continuously joining or leaving, resulting in shifting Nash equilibria and frequent disruptions of equality constraints. This inherent instability poses a significant challenge to traditional incremental-consensus-based distributed optimization or game methods, which rely on a stable and consistent agent population to compute and maintain equilibrium solutions effectively. The necessity for these methods to continuously enforce constraints and the time-intensive process of recalculating equilibria in response to agent dynamics present a substantial bottleneck in the optimization of OMASs. To address this challenge, we develop an innovative incremental consensus-based distributed (ICBD) algorithm to achieve the dynamic Nash equilibrium (NE) for constrained noncooperative game of OMASs. The ICBD algorithm leverages predefined-time stability and integral sliding-mode control to enable rapid recalibration to new equilibria and maintain constraints without the need for prolonged recalculations. Finally, several numerical simulations validate our approach to demonstrating its effectiveness.