Adaptive generalized Nash equilibrium seeking algorithm for nonsmooth aggregative game under dynamic event-triggered mechanism

This paper addresses a nonsmooth aggregative game to control multiple noncooperative players, each with a nonsmooth cost function that depends not only on its own decision but also on some aggregate effect among all the agents. In addition, the decision of each player is restricted by private and coupling constraints. To address these concerns, a distributed generalized Nash equilibrium (GNE) seeking algorithm is proposed. Two features distinguish our methods from the existing GNE seeking algorithms. Firstly, an adaptive penalty method is introduced to drive each player's action to enter the set of private constraints. The adaptive term ensures automatic adjustment of penalty parameter based on the degree of constraint violation excluding any prior calculation. Secondly, a distributed dynamic event-triggered mechanism is designed for each player to lessen communication energy. In comparison to the static event-triggered mechanism, the proposed dynamic mechanism possesses larger inter-execution time intervals. As the discontinuity of the event-triggered mechanism can impact the existence of a solution to the closed-loop system in the classical sense, we adapt a nonsmooth analysis technique, including differential inclusion and Filippov solution. Through nonsmooth Lyapunov analysis, the convergence result and the avoidance of Zeno behavior are established. Finally, two engineering examples are provided to demonstrate the validity of the theoretical results.