3 research outputs found
A Neural-Network based Approach for Nash Equilibrium Seeking in Mixed-order Multi-player Games
Noticing that agents with different dynamics may work together, this paper
considers Nash equilibrium computation for a class of games in which
first-order integrator-type players and second-order integrator-type players
interact in a distributed network. To deal with this situation, we firstly
exploit a centralized method for full information games. In the considered
scenario, the players can employ its own gradient information, though it may
rely on all players' actions. Based on the proposed centralized algorithm, we
further develop a distributed counterpart. Different from the centralized one,
the players are assumed to have limited access into the other players' actions.
In addition, noticing that unmodeled dynamics and disturbances are inevitable
for practical engineering systems, the paper further considers games in which
the players' dynamics are suffering from unmodeled dynamics and time-varying
disturbances. In this situation, an adaptive neural network is utilized to
approximate the unmodeled dynamics and disturbances, based on which a
centralized Nash equilibrium seeking algorithm and a distributed Nash
equilibrium seeking algorithm are established successively. Appropriate
Lyapunov functions are constructed to investigate the effectiveness of the
proposed methods analytically. It is shown that if the considered mixed-order
game is free of unmodeled dynamics and disturbances, the proposed method would
drive the players' actions to the Nash equilibrium exponentially. Moreover, if
unmodeled dynamics and disturbances are considered, the players' actions would
converge to arbitrarily small neighborhood of the Nash equilibrium. Lastly, the
theoretical results are numerically verified by simulation examples