Distributed Robust Predefined-Time Algorithm for Seeking Nash Equilibrium in MASs

Dear Editor, This letter presents a solution to the problem of seeking Nash equilibrium (NE) in a class of non-cooperative games of multi-agent systems (MASs) subject to the input disturbance and the networked communication. To this end, a novel distributed robust predefined-time algorithm is proposed, which ensures the precise convergence of agent states to the NE within a settling time that can be directly determined by adjusting one or more parameters. The proposed algorithm employs an integral sliding mode strategy to effectively reject disturbances. Additionally, a consensus-based estimator is designed to overcome the challenge of limited information availability, where each agent can only access information from its directly connected neighbors, which conflicts with the computation of the cost function that requires information from all agents. Finally, a numerical example is provided to demonstrate the algorithm's effectiveness and performance.