Dynamic self-triggered algorithm for distributed Nash equilibrium seeking in constrained multi-agent games

Abstract

This paper investigates the distributed dynamic self-triggered Nash equilibrium seeking problem for constrained multi-agent games, where the action of each agent is subject to local inequality constraints. A three-part distributed Nash equilibrium seeking strategy is first developed by integrating a tracking controller, a projected gradient play, and a leader-following protocol. To ensure that the state of each agent always remains within the constrained set, a key lemma is established to predict the time instant at which an agent’s state would leave the constrained set. Based on this lemma, a new dynamic self-triggered algorithm is proposed to eliminate the need for continuous measurement, computation, and communication among agents. Moreover, it is shown that, under the proposed strategy, the actions of all agents always satisfy the local inequality constraints and converge exponentially to the Nash equilibrium. In addition, we prove that Zeno behavior is excluded. Finally, two examples are provided to verify the effectiveness of the theoretical results.