Predefined-time event-triggered generalized Nash equilibrium seeking for aggregative games and its application to smart charging system

Motivated by resource allocation problems in competitive multi-generator systems, this paper addresses predefined-time generalized Nash equilibrium (GNE) seeking for aggregative games with coupling equality constraints. To realize high-speed GNE computation while decreasing the interaction burden, a distributed predefined-time GNE seeking algorithm with discrete-time interaction is designed. Unlike existing research on GNE seeking with asymptotic convergence, a novel time base generator (TBG) is introduced into the algorithm to achieve the predefined-time GNE computation. Moreover, considering the aggregative structure of payoff functions, a novel average tracking technique is adopted to ensure each agent's actual evaluation of the aggregative term in a distributed manner within the predefined time. By virtue of a dynamic event-triggered mechanism (DETM), agents' interaction burden is effectively reduced while the predefined-time convergence of the algorithm is maintained. Finally, the smart charging system for electric vehicles is employed to provide an effective power output scheme.