Distributed Nash Equilibrium Computation With Uncertain Dynamics and Disturbances

Nash equilibrium computation problems under distributed communication scenarios are addressed in this paper. In particular, the players, including first- and second-order ones, are considered to be affected by unknown disturbances and dynamics. To accommodate this problem, the followings need to be simultaneously achieved: (1) Distributed estimation of unknown information needed for optimizing the players' objective functions; (2) The optimization of the players' objective functions; and (3) Dynamics stabilization for the players, especially for the accommodation of unknown disturbances and dynamics. Based on first-order low-pass filters, an unknown dynamics estimator is established (for the estimation of unknown dynamics and disturbances), by which distributed computing methods are constructed by further employing gradient-like optimization components (for optimizing the players' objective functions) and consensus components (for distributed action estimation). The presented analytical investigation shows that the players' actions and velocities (for second-order players) can converge into a small ball around the Nash equilibrium and zero respectively by choosing the control parameters properly according to the given rules. Moreover, the proposed algorithm is adapted to address connectivity control of mobile sensors. Numerical verification is provided by utilizing KUKA YouBot vehicles in V-REP.